# String Transmission

### Problem Statement :

```Bob has received a binary string of length N transmitted by Alice. He knows that due to errors in transmission, up to K bits might have been corrupted (and hence flipped). However, he also knows that the string Alice had intended to transmit was not periodic. A string is not periodic if it cannot be represented as a smaller string concatenated some number of times. For example, "0001", "0110" are not periodic while "00000", "010101" are periodic strings.

Now he wonders how many possible strings could Alice have transmitted.

Input Format

The first line contains the number of test cases T. T test cases follow. Each case contains two integers N and K on the first line, and a binary string of length N on the next line.

Output Format

Output T lines, one for each test case. Since the answers can be really big, output the numbers modulo 1000000007.```

### Solution :

```                            ```Solution in C :

In C :

#include <stdlib.h>
#include <stdio.h>
int N,K;
int F[1000][1000],S[1000];
char s[1001];
int f(int x, int i, int j) {
if(j>K) return 0;
if(i==x) return 1;
if(F[i][j]==-1) F[i][j] = (f(x,i+1,j+S[i])+f(x,i+1,j+N/x-S[i]))%1000000007;;
return F[i][j];
}
int g(int x, int *p) {
if((*p)!=0) return (g(x,p+1)-g(x/(*p),p+1))%1000000007;
int i,j;
for(i=0; i<x; i++) for(j=0; j<=K; j++) F[i][j] = -1;
for(i=0; i<x; i++) {
S[i] = 0;
for(j=i; j<N; j+=x) S[i]+= (s[j]=='1')?1:0;
}
return f(x,0,0);
}
int main() {
int i,j,k,T;
int ps[170],l[500],p[5];
for(i=0;i<500;i++) l[i] = 1;
ps[0] = 2;
for(i=3,k=1;i<1000;i+=2) if(l[i/2]) {
ps[k++] = i;
for(j=i*i/2;j<500;j+=i) l[j] = 0;
}
scanf("%d",&T);
for(;T>0;T--) {
scanf("%d %d %[01]",&N,&K,s);
for(i=0,j=0; i<k; i++) if(N%ps[i]==0) p[j++] = ps[i];
p[j] = 0;
printf("%d\n",(g(N,p)+1000000007)%1000000007);
}
exit(0);
}```
```

```                        ```Solution in C++ :

In  C ++  :

#include <cstdio>
#include <cstring>

const int mod = 1000000007;

#define MAXN 1005

int T, N, K;
char b[ MAXN ];

int c[ MAXN ][ MAXN ];
int cnt[ MAXN ][ 2 ];
int dp[ MAXN ];
int p[ MAXN ];

int main( void )
{
scanf( "%d", &T );

for( int i = 0; i < MAXN; ++i ) {
for( int j = 0; j < MAXN; ++j ) {
if( j > i ) continue;
if( i == 0 ) { c[i][j] = 1; continue; }
c[i][j] = c[i-1][j] + c[i-1][j-1];
if( c[i][j] > mod ) c[i][j] -= mod;
}
}

while( T-- ) {
scanf( "%d%d", &N, &K );
scanf( "%s", b );

for( int i = 1; i < N; ++i )
p[i] = 0;

int periodic = 0;

for( int i = 1; i < N; ++i ) {
if( N % i != 0 ) continue;

for( int j = 0; j < i; ++j )
cnt[j][0] = cnt[j][1] = 0;

for( int j = 0; j < N; ++j )
cnt[j%i][1-b[j]+'0']++;

for( int j = 0; j <= K; ++j )
dp[j] = 1;

for( int j = 0; j < i; ++j ) {
for( int k = K; k >= 0; --k ) {
dp[k] = ( !cnt[j][0] || !cnt[j][1] ) ? dp[k] : 0;
if( k >= cnt[j][0] && cnt[j][0] ) dp[k] += dp[k-cnt[j][0]];
if( k >= cnt[j][1] && cnt[j][1] ) dp[k] += dp[k-cnt[j][1]];
if( dp[k] > mod ) dp[k] -= mod;
}
}

p[i] = dp[K];

for( int j = 1; j < i; ++j ) {
if( i % j == 0 ) p[i] = p[i] + mod - p[j];
if( p[i] > mod ) p[i] -= mod;
}

periodic += p[i];
if( periodic >= mod ) periodic -= mod;
}

int total = 0;

for( int i = 0; i <= K; ++i ) {
total += c[N][i];
if( total >= mod ) total -= mod;
}

int Sol = total - periodic + mod;
if( Sol >= mod ) Sol -= mod;

printf( "%d\n", Sol );
}

return 0;
}```
```

```                        ```Solution in Java :

In  Java :

import java.io.*;
import java.util.HashSet;
import java.util.Set;
import java.util.StringTokenizer;

public class Solution implements Runnable {

// leave empty to read from stdin/stdout
private static final String TASK_NAME_FOR_IO = "";

// file names
private static final String FILE_IN = TASK_NAME_FOR_IO + ".in";
private static final String FILE_OUT = TASK_NAME_FOR_IO + ".out";

PrintWriter out;
StringTokenizer tokenizer = new StringTokenizer("");

public static void main(String[] args) {
new Solution().run();
}

final long MOD = 1000000007L;

int N_MAX = 1005;
long[][] cnk = new long[N_MAX][N_MAX];

private void solve() throws IOException {
for (int n = 0; n < N_MAX; n++) {
cnk[n][0] = 1;
cnk[n][n] = 1;
for (int k = 1; k < n; k++) {
cnk[n][k] = cnk[n - 1][k - 1] + cnk[n - 1][k];
cnk[n][k] %= MOD;
}
}

/*
System.out.println("int[][] COEFF = new int[][] {");
for (int n = 0; n <= 1000; n++) {
fastPrecalc(n);
}
System.out.println("};");
*/

/*
Random r = new Random();
for (int n = 1; n <= 50; n++) {
System.out.println("N=" + n);
for (int d = 0; d <= 4; d++)
for (int attempts = 0; attempts < 20; attempts++) {
long mask = r.nextLong() & (1L << 3);

for (int j = 0; j < n; j++) {
num >>= 1;
}

long a = naive(n, d, maskC.toCharArray());
long b = fast(n, d, maskC.toCharArray());

if (a != b) {
System.err.println(n + " - " + d + " - " + maskC + "(" + a + " vs. " + b + ", delta " + (a - b) + ")");
}
}
}

for (int n = 1; n <= 1000; n++) {
for (int j = 0; j < n; j++) {
}

long b = fast(n, 0, maskC.toCharArray());
if (b > 0) {
System.err.println(n + " - " + b);
}
}
*/

int tc = nextInt();
for (int tcIdx = 0; tcIdx < tc; tcIdx++) {
int n = nextInt();
int maxD = nextInt();
char[] c = nextToken().toCharArray();

out.println(fast(n, maxD, c));
}
}

static int gcd(int a, int b) {
if (b == 0) {
return a;
} else {
return gcd(b, a % b);
}
}

static int MAX_GCD_NUM = 1005;
static int[][] GCD_STATIC = new int[MAX_GCD_NUM][MAX_GCD_NUM];

static {
for (int i = 0; i < MAX_GCD_NUM; i++)
for (int j = 0; j <= i; j++) {
int g = gcd(i, j);
GCD_STATIC[i][j] = g;
GCD_STATIC[j][i] = g;
}
}

@SuppressWarnings({"UnusedDeclaration"})
private long notFastEnough(int n, int maxD, char[] c) {

int cnt = 0;
for (int period = 1; period < n; period++) {
if (n % period == 0) {
cnt++;
}
}

int[] periods = new int[cnt];
{
int idx = 0;
for (int period = 1; period < n; period++)
if (n % period == 0) {
periods[idx++] = period;
}
}

for (int i = 0; i < cnt; i++) {
periodicAnswer[periods[i]] = countPeriodic(n, maxD, periods[i], c);
}

// calculate total
long total = 0;
for (int i = 0; i <= maxD; i++) {
total += cnk[n][i];
total %= MOD;
}

// calculate partial gcd
int lBits = cnt / 2;
int lBits2 = 1 << lBits;
int[] lGcd = new int[lBits2];

{
int common = -1;
for (int i = 0; i < lBits; i++)
if ((mask & (1 << i)) != 0) {
common = (common == -1) ? periods[i] : GCD_STATIC[common][periods[i]];
if (common == 1) {
break;
}
}
}
}

int rBits = cnt - lBits;
int rBits2 = 1 << rBits;

int[] rGcd = new int[rBits2];
{
int common = -1;
for (int i = 0; i < rBits; i++)
if ((mask & (1 << i)) != 0) {
common = (common == -1) ? periods[i + lBits] : GCD_STATIC[common][periods[i + lBits]];
if (common == 1) {
break;
}
}
}
}

long cnt2 = 1L << cnt;
// determine sign by the number of bits in the mask
int sign = (bitCount(mask) & 1) == 0 ? 1 : -1;

// fast calculate gcd by analysing left and right part
int gcdLeft = lGcd[(int) (mask & (lBits2 - 1))];
int gcdRight = rGcd[(int) (mask >> lBits)];

int common;
if (gcdLeft == -1) {
common = gcdRight;
} else if (gcdRight == -1) {
common = gcdLeft;
} else {
common = GCD_STATIC[gcdLeft][gcdRight];
}

/*
int common = -1;
for (int i = 0; i < cnt; i++)
if ((mask & (1 << i)) != 0) {
common = (common == -1) ? periods[i] : GCD_STATIC[common][periods[i]];
if (common == 1) {
break;
}
}
*/

total %= MOD;
}

total %= MOD;
total += MOD;
total %= MOD;

}

private long fast(int n, int maxD, char[] c) {

int cnt = 0;
for (int period = 1; period < n; period++) {
if (n % period == 0) {
cnt++;
}
}

int[] periods = new int[cnt];
{
int idx = 0;
for (int period = 1; period < n; period++)
if (n % period == 0) {
periods[idx++] = period;
}
}

for (int i = 0; i < cnt; i++) {
periodicAnswer[i] = countPeriodic(n, maxD, periods[i], c);
}

// calculate total
long total = 0;
for (int i = 0; i <= maxD; i++) {
total += cnk[n][i];
total %= MOD;
}

int[] coeff = COEFF[n];
if (coeff.length != cnt) {
throw new IllegalStateException("INVALID STATE");
}

for (int i = 0; i < cnt; i++) {
total %= MOD;
}

total %= MOD;
total += MOD;
total %= MOD;

}

int[][] COEFF = new int[][] {
{},
{},
{-1,},
{-1,},
{0,-1,},
{-1,},
{1,-1,-1,},
{-1,},
{0,0,-1,},
{0,-1,},
{1,-1,-1,},
{-1,},
{0,1,0,-1,-1,},
{-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,-1,},
{-1,},
{0,0,1,-1,-1,},
{-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{-1,},
{0,0,0,1,0,-1,-1,},
{0,-1,},
{1,-1,-1,},
{0,0,-1,},
{0,1,-1,0,-1,},
{-1,},
{-1,1,1,1,-1,-1,-1,},
{-1,},
{0,0,0,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,1,0,-1,-1,},
{-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,1,0,-1,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,1,-1,0,-1,},
{0,1,0,-1,-1,},
{1,-1,-1,},
{-1,},
{0,0,0,0,0,1,0,-1,-1,},
{0,-1,},
{0,0,1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{-1,},
{0,0,0,0,1,-1,-1,},
{1,-1,-1,},
{0,0,1,0,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{-1,},
{0,-1,0,1,0,1,1,-1,0,-1,-1,},
{-1,},
{1,-1,-1,},
{0,1,0,-1,-1,},
{0,0,0,0,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{-1,1,1,1,-1,-1,-1,},
{-1,},
{0,0,0,0,0,0,0,1,0,-1,-1,},
{-1,},
{1,-1,-1,},
{0,0,1,-1,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,0,0,0,1,0,-1,0,-1,},
{0,0,0,-1,},
{1,-1,-1,},
{-1,},
{0,-1,0,1,1,0,-1,1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,1,-1,0,0,-1,},
{-1,},
{0,0,-1,0,1,1,0,1,-1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,0,1,0,-1,-1,},
{-1,},
{0,0,1,-1,-1,},
{0,1,-1,0,-1,},
{0,0,0,0,1,-1,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,0,1,-1,0,0,-1,},
{-1,1,1,1,-1,-1,-1,},
{1,-1,-1,},
{-1,},
{0,0,0,0,0,0,0,1,0,-1,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,1,0,-1,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,-1,0,0,1,0,1,0,1,-1,0,-1,-1,},
{0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{0,0,-1,},
{0,0,-1,1,0,1,0,-1,1,-1,-1,},
{-1,},
{0,0,0,0,0,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,-1,0,1,1,0,-1,1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,1,0,-1,-1,},
{0,0,1,-1,0,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,-1,1,0,0,1,1,-1,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,0,0,0,0,1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,1,-1,-1,},
{0,1,-1,0,-1,},
{-1,},
{0,0,0,-1,0,1,1,1,-1,-1,-1,},
{-1,},
{0,0,1,-1,0,0,-1,},
{0,1,-1,0,-1,},
{-1,1,1,1,-1,-1,-1,},
{1,-1,-1,},
{0,-1,0,1,1,-1,0,1,0,-1,-1,},
{-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,1,0,-1,0,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,1,-1,-1,},
{-1,},
{0,1,-1,0,-1,},
{-1,1,1,1,-1,-1,-1,},
{1,-1,-1,},
{-1,},
{0,0,0,-1,0,0,1,1,0,0,-1,1,0,-1,-1,},
{0,-1,},
{-1,1,1,-1,1,-1,-1,},
{0,1,-1,0,-1,},
{0,1,-1,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{0,1,0,-1,-1,},
{0,0,0,1,0,-1,0,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{-1,},
{0,0,0,0,0,-1,0,0,1,0,1,0,1,-1,0,-1,-1,},
{-1,},
{-1,1,1,1,-1,-1,-1,},
{1,-1,-1,},
{0,0,1,-1,0,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{0,0,0,1,0,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,0,0,0,0,0,0,0,0,1,0,-1,-1,},
{-1,},
{1,-1,-1,},
{-1,1,1,1,-1,-1,-1,},
{0,0,0,0,1,-1,0,-1,},
{-1,},
{0,0,-1,1,1,0,-1,0,1,-1,-1,},
{-1,},
{0,0,0,0,0,0,1,0,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,-1,0,1,1,-1,0,1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{0,0,0,1,0,-1,0,0,-1,},
{1,-1,-1,},
{1,-1,-1,-1,1,-1,1,1,1,1,-1,1,-1,-1,-1,},
{-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,0,0,0,0,0,1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,-1,1,0,1,0,-1,1,-1,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,0,0,0,0,0,1,0,-1,0,-1,},
{0,0,0,0,1,0,-1,-1,},
{1,-1,-1,},
{-1,},
{0,-1,0,1,1,-1,0,1,0,-1,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,1,1,1,-1,-1,-1,},
{0,0,1,-1,0,0,-1,},
{-1,},
{0,0,-1,1,1,0,-1,0,1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,0,0,0,0,0,-1,0,0,0,1,0,1,0,1,-1,0,-1,-1,},
{-1,},
{0,0,1,-1,-1,},
{0,0,0,0,-1,},
{0,1,-1,0,-1,},
{0,0,1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,1,-1,0,0,-1,},
{1,-1,-1,},
{0,0,0,0,1,-1,-1,},
{-1,},
{0,0,0,0,-1,0,0,1,0,1,0,0,-1,1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{0,0,0,0,0,0,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,-1,1,0,1,0,-1,1,-1,0,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{-1,},
{0,0,0,-1,0,1,0,1,0,-1,0,1,0,-1,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{-1,},
{0,0,0,0,0,-1,0,0,1,1,0,1,-1,-1,-1,},
{-1,},
{0,0,0,1,-1,0,0,0,-1,},
{-1,1,1,1,-1,-1,-1,},
{1,-1,-1,},
{0,1,0,-1,-1,},
{0,-1,0,1,1,-1,0,1,0,-1,-1,},
{-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{0,0,-1,0,0,1,0,0,1,1,0,-1,-1,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,1,-1,0,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,1,1,1,-1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,-1,},
{0,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{-1,},
{0,0,0,0,-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,1,-1,0,0,-1,},
{0,0,1,0,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,-1,0,0,1,0,1,1,-1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,1,-1,0,0,0,-1,},
{1,-1,-1,},
{0,0,-1,1,1,0,-1,0,1,-1,-1,},
{-1,},
{0,-1,1,0,0,1,1,-1,-1,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,0,0,-1,0,1,1,0,-1,0,0,1,0,-1,-1,},
{-1,},
{1,-1,-1,},
{0,-1,0,0,1,1,1,0,-1,-1,-1,},
{0,1,-1,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,0,0,1,0,-1,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
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{1,-1,-1,},
{0,-1,0,1,1,-1,0,1,0,-1,-1,},
{-1,1,1,1,-1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,1,-1,0,0,-1,},
{-1,},
{0,0,0,0,0,0,0,0,0,-1,0,0,1,1,0,1,-1,-1,-1,},
{-1,},
{0,-1,1,0,1,-1,0,1,-1,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,-1,0,1,0,1,0,-1,0,0,0,1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,-1,0,1,0,1,1,-1,0,-1,-1,},
{0,-1,1,0,1,-1,0,1,-1,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,0,1,-1,0,0,-1,},
{0,0,-1,0,1,1,0,1,-1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,0,0,0,-1,0,1,1,0,-1,0,0,0,1,0,-1,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,0,1,0,-1,0,0,-1,},
{0,1,0,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,-1,1,0,0,1,1,-1,-1,0,-1,},
{0,0,1,-1,0,0,-1,},
{1,-1,-1,},
{-1,},
{0,0,0,1,0,0,0,-1,0,-1,0,0,-1,0,1,-1,0,0,1,0,1,1,0,1,0,-1,1,-1,0,-1,-1,},
{0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{0,0,1,-1,-1,},
{0,0,-1,1,1,-1,0,0,1,-1,-1,},
{0,0,1,-1,-1,},
{0,0,0,1,-1,0,0,0,-1,},
{1,-1,-1,},
{0,0,-1,1,0,1,0,-1,1,-1,-1,},
{1,-1,-1,},
{0,-1,0,1,1,-1,0,1,0,-1,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{0,-1,0,1,1,0,-1,1,0,-1,-1,},
{0,0,1,-1,0,0,-1,},
{-1,},
{1,-1,-1,1,-1,-1,1,1,1,1,-1,-1,1,-1,-1,},
{-1,},
{0,-1,1,0,1,-1,0,1,-1,0,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{-1,},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,1,-1,-1,},
{0,-1,1,0,1,-1,0,1,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,-1,1,1,1,-1,-1,1,1,1,-1,-1,-1,},
{1,-1,-1,},
{0,0,1,-1,0,0,-1,},
{0,1,-1,0,-1,},
{-1,1,1,1,-1,-1,-1,},
{0,0,0,1,0,-1,-1,},
{0,-1,0,1,1,-1,0,1,0,-1,-1,},
{-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,-1,0,0,1,0,0,1,0,0,-1,1,0,-1,0,-1,},
{-1,},
{0,0,0,0,0,0,0,0,-1,1,0,1,0,-1,1,-1,-1,},
{-1,},
{0,-1,1,0,0,1,1,-1,-1,0,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{-1,},
{0,0,0,-1,0,1,1,-1,0,0,0,1,0,-1,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{0,0,0,0,1,0,-1,0,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,0,0,0,0,1,0,-1,0,-1,},
{-1,1,1,1,-1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,1,0,1,-1,0,-1,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{0,0,1,-1,0,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,1,-1,0,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,-1,1,-1,1,1,1,1,-1,1,-1,-1,-1,},
{-1,},
{0,0,0,0,0,-1,0,1,0,1,0,-1,0,0,0,1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{0,0,0,0,-1,0,1,1,0,0,-1,0,1,-1,-1,},
{-1,},
{0,0,-1,0,1,0,1,0,-1,0,1,0,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,1,0,-1,-1,0,0,1,-1,0,-1,1,0,1,1,1,0,-1,-1,1,0,-1,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{0,0,0,0,1,0,-1,0,0,0,-1,},
{-1,},
{1,-1,-1,-1,1,1,1,-1,-1,1,1,1,-1,-1,-1,},
{0,1,0,-1,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,},
{-1,1,1,1,-1,-1,-1,},
{0,0,0,0,0,0,0,-1,0,0,1,0,1,0,0,-1,0,0,0,1,0,-1,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,-1,1,0,1,-1,0,1,-1,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,0,1,-1,0,0,0,-1,},
{0,0,0,0,-1,0,0,1,0,1,1,0,-1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,-1,0,1,1,-1,0,1,0,-1,-1,},
{1,-1,-1,},
{0,0,-1,1,0,1,0,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,-1,0,1,0,0,1,0,-1,1,0,-1,0,-1,},
{-1,},
{0,0,-1,1,1,-1,0,0,1,-1,-1,},
{1,-1,-1,},
{0,1,-1,0,-1,},
{-1,1,1,1,-1,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,0,0,0,0,0,0,0,0,-1,0,0,0,1,0,1,0,1,-1,0,-1,-1,},
{0,-1,},
{-1,1,1,-1,1,-1,-1,},
{0,1,-1,0,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,},
{-1,},
{0,0,0,0,0,0,1,-1,0,0,-1,},
{-1,1,1,1,-1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{-1,},
{0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,-1,-1,},
{1,-1,-1,},
{1,-1,-1,},
{0,0,-1,0,1,1,0,1,-1,-1,-1,},
{0,0,0,1,-1,0,0,0,-1,},
{-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,0,0,0,0,0,-1,0,1,0,0,1,1,-1,-1,0,-1,},
{0,1,-1,0,-1,},
{1,-1,-1,},
{-1,},
{0,0,0,-1,0,1,1,-1,0,0,0,1,0,-1,-1,},
{1,-1,-1,},
{-1,1,1,1,-1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{0,-1,1,0,0,1,1,-1,-1,0,-1,},
{1,-1,-1,},
{0,0,1,0,-1,-1,0,0,-1,1,0,1,-1,1,0,1,-1,1,0,1,-1,-1,-1,},
{-1,},
{0,0,0,0,1,0,-1,0,0,0,-1,},
{1,-1,-1,},
{-1,1,1,-1,1,-1,-1,},
{1,-1,-1,},
{0,-1,0,1,1,-1,0,1,0,-1,-1,},
{-1,},
{1,-1,-1,},
{0,0,1,-1,0,0,-1,},
{0,0,0,0,0,0,0,0,0,0,1,0,-1,0,-1,},
};

private void fastPrecalc(int n) {

int cnt = 0;
for (int period = 1; period < n; period++) {
if (n % period == 0) {
cnt++;
}
}

int[] periods = new int[cnt];
{
int idx = 0;
for (int period = 1; period < n; period++)
if (n % period == 0) {
periods[idx++] = period;
}
}

if (cnt > 30) {
System.err.println("N = " + n + ", CNT = " + cnt);
}

long cnt2 = 1L << cnt;
long[] coeff = new long[cnt];
// determine sign by the number of bits in the mask
int sign = (bitCount(mask) & 1) == 0 ? 1 : -1;

int common = -1;
for (int i = 0; i < cnt; i++)
if ((mask & (1L << i)) != 0) {
common = (common == -1) ? periods[i] : gcd(common, periods[i]);
if (common == 1) {
break;
}
}

int j = -1;
for (int i = 0; i < cnt; i++)
if (periods[i] == common) {
j = i;
break;
}

coeff[j] += sign;
}

System.out.print("  {");
for (int i = 0; i < cnt; i++) {
System.out.print(coeff[i] + ",");
}
System.out.println("},");
}

private long countPeriodic(int n, int maxD, int period, char[] c) {
int[] zeroes = new int[period];
int[] ones = new int[period];
for (int i = 0; i < period; i++) {
int j = i;
while (j < n) {
if (c[j] != '0') {
ones[i]++;
} else {
zeroes[i]++;
}
j += period;
}
}

long[][] d = new long[period + 1][maxD + 1];
d[0][maxD] = 1;
for (int i = 0; i < period; i++)
for (int remD = 0; remD <= maxD; remD++)
if (d[i][remD] > 0) {
// replace zeroes with ones
if (remD - zeroes[i] >= 0) {
d[i + 1][remD - zeroes[i]] += d[i][remD];
d[i + 1][remD - zeroes[i]] %= MOD;
}

// replace ones with zeroes
if (remD - ones[i] >= 0) {
d[i + 1][remD - ones[i]] += d[i][remD];
d[i + 1][remD - ones[i]] %= MOD;
}
}

long result = 0;
for (int i = 0; i <= maxD; i++) {
result += d[period][i];
result %= MOD;
}
return result;
}

@SuppressWarnings({"UnusedDeclaration"})
private long naive(int n, int maxD, char[] c) {
}

private boolean isPeriodic(int n, long mask) {
for (int period = 1; period < n; period++)
if (n % period == 0 && isPeriodic(n, mask, period)) {
return true;
}
return false;
}

private boolean isPeriodic(int n, long mask, int period) {
for (int i = 0; i < period; i++) {
boolean bitHere = (mask & (1L << i)) != 0;

int j = i;
while (j < n) {
boolean bitThere = (mask & (1L << j)) != 0;
if (bitHere != bitThere) {
return false;
}
j += period;
}
}

return true;
}

@SuppressWarnings({"UnusedDeclaration"})
private long naive1(int n, int maxD, long c) {
long result = 0;
long n2 = 1 << n;
result++;
}
}
return result;
}

@SuppressWarnings({"UnusedDeclaration"})
private long naive2(int n, int maxD, long c) {
Set<Long> periodic = new HashSet<Long>();

// count only periodic
for (int periodLength = 1; periodLength < n; periodLength++)
if (n % periodLength == 0) {
int periodTimes = n / periodLength;

long p2 = 1L << periodLength;
for (int i = 0; i < periodTimes; i++) {
}

// see if it is applicable
if (distinctBits(n, totalMask, c) <= maxD) {
}
}
}

int total = 0;
for (int k = 0; k <= maxD; k++) {
total += cnk[n][k];
}

}

private long naive3(int n, int maxD, long c) {
long total = 0;
for (int k = 0; k <= maxD; k++) {
total += cnk[n][k];
}

}

private long periodicGen(int pos, int n, int maxD, long c) {
if (pos >= n) {
return isPeriodic(n, c) ? 1 : 0;
}
long total = periodicGen(pos + 1, n, maxD, c);
if (maxD > 0) {
total += periodicGen(pos + 1, n, maxD - 1, c ^ (1L << pos));
}
}

static int BIT_COUNT_LIMIT_POW = 18;
static int BIT_COUNT_LIMIT_MASK = (1 << BIT_COUNT_LIMIT_POW) - 1;
static int[] BIT_COUNT = new int[1 << BIT_COUNT_LIMIT_POW];

static {
for (int i = 1; i < BIT_COUNT.length; i++)
BIT_COUNT[i] = BIT_COUNT[i & (i - 1)] + 1;
}

@SuppressWarnings({"UnusedParameters"})
private int distinctBits(int n, long m1, long m2) {
return bitCount(m1 ^ m2);
}

}

long result = 0;
for (char v : c) {
result <<= 1;
result += v - '0';
}
return result;
}

public void run() {
long timeStart = System.currentTimeMillis();

boolean fileIO = TASK_NAME_FOR_IO.length() > 0;
try {

if (fileIO) {
out = new PrintWriter(new FileWriter(FILE_OUT));
} else {
out = new PrintWriter(new OutputStreamWriter(System.out));
}

solve();

in.close();
out.close();
} catch (IOException e) {
throw new IllegalStateException(e);
}
long timeEnd = System.currentTimeMillis();

if (fileIO) {
System.out.println("Time spent: " + (timeEnd - timeStart) + " ms");
}
}

private String nextToken() throws IOException {
while (!tokenizer.hasMoreTokens()) {
if (line == null) {
return null;
}
tokenizer = new StringTokenizer(line);
}
}

private int nextInt() throws IOException {
return Integer.parseInt(nextToken());
}

}```
```

```                        ```Solution in Python :

In  Python3 :

T = int(input())
M = 1000000007

from math import factorial, sqrt

def nck(n, k):
res = 0

for i in range(k+1):
res += factorial(n)//(factorial(i)*factorial(n-i))
return res

def divisors(n):
d1 = [1]
d2 = []
for i in range(2, int(sqrt(n)) + 1):
if n % i == 0:
d1.append(i)
if i*i != n:
d2.append(n//i)
d1.extend(d2[::-1])
return d1

for _ in range(T):

N, K = [int(x) for x in input().split()]
S = input()
if N == 1:
print(N+K)
continue

total = nck(N, K)
div = divisors(N)
dp = [[0]*(N+K+1) for i in range(len(div))]
is_periodic = False

for i, d in enumerate(div):
dp[i][0] = 1
for offset in range(d):
zeros = 0

for j in range(offset, N, d):
if S[j] == "0":
zeros += 1
ones = N//d - zeros

prev = list(dp[i])
dp[i][:] = [0]*(N+K+1)

for k in range(K+1):
if prev[k]:
dp[i][k + zeros] += prev[k]
dp[i][k + ones] += prev[k]

if dp[i][0]:
is_periodic = True

for i2 in range(i):
d2 = div[i2]
if d % d2 == 0:
for k in range(K+1):
dp[i][k] -= dp[i2][k]

for k in range(1, K+1):
total -= dp[i][k]

print((total-is_periodic) % M)```
```

## Insert a node at a specific position in a linked list

Given the pointer to the head node of a linked list and an integer to insert at a certain position, create a new node with the given integer as its data attribute, insert this node at the desired position and return the head node. A position of 0 indicates head, a position of 1 indicates one node away from the head and so on. The head pointer given may be null meaning that the initial list is e

## Delete a Node

Delete the node at a given position in a linked list and return a reference to the head node. The head is at position 0. The list may be empty after you delete the node. In that case, return a null value. Example: list=0->1->2->3 position=2 After removing the node at position 2, list'= 0->1->-3. Function Description: Complete the deleteNode function in the editor below. deleteNo

## Print in Reverse

Given a pointer to the head of a singly-linked list, print each data value from the reversed list. If the given list is empty, do not print anything. Example head* refers to the linked list with data values 1->2->3->Null Print the following: 3 2 1 Function Description: Complete the reversePrint function in the editor below. reversePrint has the following parameters: Sing