# Fibonacci Numbers Tree

### Problem Statement :

```Shashank loves trees and math. He has a rooted tree, T , consisting of N nodes uniquely labeled with integers in the inclusive range [1 , N ]. The node labeled as 1 is the root node of tree , and each node in  is associated with some positive integer value (all values are initially ).

Let's define Fk as the Kth  Fibonacci number. Shashank wants to perform 22 types of operations over his tree, T:

1. UXK
Update the subtree rooted at node X such that the node at level 0 in subtree X (i.e., node X) will have  Fk added to it, all the nodes at level 1 will have Fk+1  added to them, and so on. More formally, all the nodes at a distance D  from node X  in the subtree of node  X will have the ( k - D)th Fibonacci number added to them.

2. QXY
Find the sum of all values associated with the nodes on the unique path from X  to  Y . Print your sum modulo  10^9 + 7 on a new line.
Given the configuration for tree T and a list of M  operations, perform all the operations efficiently.

Note: .F1 = F2 = 1.

Input Format

The first line contains 2  space-separated integers, N (the number of nodes in tree T) and M (the number of operations to be processed), respectively.
Each line i  of the N-1  subsequent lines contains an integer, P, denoting the parent of the ( i -1 )th node.
Each of the M subsequent lines contains one of the two types of operations mentioned in the Problem Statement above.

Constraints

1  <=  N, M  <=  10^5
1  <=  X,  Y  <=  N
1  <=  k  <=  10^15

Output Format

For each operation of type  2(i.e.,Q ), print the required answer modulo 10^9 + 7 on a new line.```

### Solution :

```                            ```Solution in C :

In    C++  :

#include<iostream>
#include<cstdio>
#include<algorithm>
#include<set>
#include<map>
#include<queue>
#include<cassert>
#define PB push_back
#define MP make_pair
#define sz(v) (in((v).size()))
#define forn(i,n) for(in i=0;i<(n);++i)
#define forv(i,v) forn(i,sz(v))
#define fors(i,s) for(auto i=(s).begin();i!=(s).end();++i)
#define all(v) (v).begin(),(v).end()
using namespace std;
typedef int in;
typedef vector<in> VI;
typedef vector<VI> VVI;
const in pmod=1000000007LL;
long long p2(long long a){
return (1LL<<a);
}
template<typename T> T pw(T a, in b){
T r=1LL;
for(long long i=30;i>=0;i--){
r*=r;
if(b&p2(i))
r*=a;
}
return r;
}
struct fp{
long long a;
fp(long long aa=0){
a=aa;
if(a<0 || a>=pmod){
a%=pmod;
if(a<0)
a+=pmod;
}
}
fp inv()const{
return pw(*this,pmod-2);
}
fp operator*(const fp cp)const{
return fp((a*cp.a)%pmod);
}
fp operator+(const fp cp)const{
return fp((a+cp.a)>pmod?a+cp.a-pmod:a+cp.a);
}
fp operator/(const fp cp)const{
return (*this)*cp.inv();
}
fp operator-(const fp cp)const{
return (*this)+(-cp);
}
fp operator-()const{
return (a==0?0:pmod-a);
}
fp& operator*=(const fp cp){
return (*this)=(*this)*cp;
}
fp& operator/=(const fp cp){
return (*this)=(*this)/cp;
}
fp& operator+=(const fp cp){
return (*this)=(*this)+cp;
}
fp& operator-=(const fp cp){
return (*this)=(*this)-cp;
}
bool operator==(const fp cp)const{
return a==cp.a;
}
bool operator!=(const fp cp)const{
return a!=cp.a;
}
};
ostream& operator<<(ostream& os, fp a){
return os<<a.a;
}
struct mat{
vector<vector<fp> > a;
in n,m;
void ini(in pn, in pm){
a.clear();
n=pn;
m=pm;
a.resize(n,vector<fp>(m,fp(0LL)));
}
mat operator*(const mat& cp)const{
assert(m==cp.n);
mat r;
r.ini(n,cp.m);
long long t;
forn(i,n){
forn(j,cp.m){
t=0;
forn(k,m){
t+=a[i][k].a*cp.a[k][j].a;
}
r.a[i][j]=t;
}
}
return r;
}
mat& operator*=(const mat& cp){
assert(m==cp.n);
mat r;
r.ini(n,cp.m);
long long t;
forn(i,n){
forn(j,cp.m){
t=0;
forn(k,m){
t+=a[i][k].a*cp.a[k][j].a;
}
r.a[i][j]=t;
}
}
return *this=r;
}
mat operator+(const mat& cp)const{
assert(n==cp.n && m==cp.m);
mat r;
r.ini(n,m);
forn(i,n){
forn(j,m){
r.a[i][j]=a[i][j]+cp.a[i][j];
}
}
return r;
}
mat& operator+=(const mat& cp){
assert(n==cp.n && m==cp.m);
forn(i,n){
forn(j,m){
a[i][j]+=cp.a[i][j];
}
}
return *this;
}
};
mat pwm(mat a, long long b){
mat r=a;
forv(i,r.a){
forv(j,r.a[i])
r.a[i][j]=(i==j);
}
bool odn=0;
for(long long i=51;i>=0;i--){
if(odn)
r*=r;
if(b&p2(i)){
odn=1;
r*=a;
}
}
return r;
}
mat basfib;
mat fibmat;
mat ttp,ts;
mat smfib,sft;
vector<mat> smpw;
pair<fp,fp> fbat(long long a){
ttp=pwm(fibmat,a-1)*basfib;
return MP(ttp.a[0][0],ttp.a[1][0]);
}
struct fenw{
vector<mat> fw;
in n;
void ini(in pn){
n=pn;
fw.clear();
fw.resize(n);
forn(i,n)
fw[i].ini(3,1);
}
in ol=l;
while(l<n){/*
mat tt=smpw[l-ol]*ts;
forv(i,tt.a){
forv(j,tt.a[i]){
cout<<tt.a[i][j]<<" ";
}
cout<<endl;
}
cout<<endl;*/
fw[l]+=smpw[l-ol]*ts;
l|=(l+1);
}
}
mat sm(in l){
mat r;
r.ini(3,1);
in ol=l;
while(l>=0){/*
mat tt=smpw[ol-l]*fw[l];
cout<<"sm "<<l<<endl;
forv(i,tt.a){
forv(j,tt.a[i]){
cout<<tt.a[i][j]<<" ";
}
cout<<endl;
}
cout<<endl;*/
r+=smpw[ol-l]*fw[l];
l&=(l+1);
--l;
}
return r;
}
};
vector<fenw> fws;
VI fid,floc;
VI sts;
const in mxp=18;
VI pr[mxp];
vector<fp> vlf,vls;
VI ht,pap;
void mkfid(in u, bool rq){
if(fid[u]!=-2)
return;
if(sts[u]*2<sts[pr[0][u]] || u==0){
if(rq==0){
fid[u]=floc[u]=-1;
return;
}
in s=sz(fws);
fws.PB(fenw());
fid[u]=s;
floc[u]=0;
return;
}
mkfid(pr[0][u],1);
fid[u]=fid[pr[0][u]];
floc[u]=floc[pr[0][u]]+1;
}
void proct(){
in n=sz(pr[0]);
sts.resize(n,1);
fid=floc=VI(n,-2);
for(in i=n-1;i>0;--i){
sts[pr[0][i]]+=sts[i];
}
for(in i=n-1;i>=0;--i){
mkfid(i,0);
}
for(in i=n-1;i>=0;--i){
if(fid[i]<0)
continue;
if(sz(fws[fid[i]].fw))
continue;
fws[fid[i]].ini(floc[i]+1);
}
pap.resize(n);
forn(i,n){
if(i==0){
pap[i]=-1;
continue;
}
if(floc[i]==0 || floc[i]==-1){
pap[i]=pr[0][i];
continue;
}
pap[i]=pap[pr[0][i]];
}
}
in lca(in u, in v){
if(ht[u]<ht[v])
swap(u,v);
for(in i=mxp-1;i>=0;--i){
if(ht[u]-p2(i)>=ht[v])
u=pr[i][u];
}
assert(ht[u]==ht[v]);
for(in i=mxp-1;i>=0;--i){
if(pr[i][u]!=pr[i][v]){
u=pr[i][u];
v=pr[i][v];
}
}
if(u!=v){
u=pr[0][u];
v=pr[0][v];
}
assert(u==v);
return u;
}
struct qel{
in u;
qel(in a=0){
u=a;
}
bool operator<(const qel& cp)const{
return ht[u]<ht[cp.u];
}
};
priority_queue<qel> q;
in vdt;
vector<mat> fv;
mat r;
vector<mat> ucm;
void clr(mat& c){
forv(i,c.a){
forv(j,c.a[i])
c.a[i][j]=0;
}
}
void prq(){
qel tel;
in tx;
while(!q.empty()){
tel=q.top();
q.pop();
tx=tel.u;
if(lvs[tx]==vdt)
continue;
lvs[tx]=vdt;
if(fid[tx]==-1){
r+=ucm[tx]*fv[tx];
if(tx==pr[0][tx]){
clr(ucm[tx]);
continue;
}
ucm[pr[0][tx]]+=smpw[1]*ucm[tx];
clr(ucm[tx]);
q.push(qel(pr[0][tx]));
}
continue;
}
r+=ucm[tx]*fws[fid[tx]].sm(floc[tx]);
if(pap[tx]==-1){
clr(ucm[tx]);
continue;
}
ucm[pap[tx]]+=smpw[floc[tx]+1]*ucm[tx];
clr(ucm[tx]);
q.push(qel(pap[tx]));
}
}
}
void ansq(in tx, in ty){
r.ini(3,1);
mat cm;
cm.ini(3,3);
forn(i,3)
cm.a[i][i]=1;
in u=lca(tx,ty);
q.push(qel(tx));
q.push(qel(ty));
q.push(qel(u));
ucm[tx]+=cm;
ucm[ty]+=cm;
forn(i,3)
cm.a[i][i]*=-1;
ucm[u]+=cm;
if(u!=0){
q.push(qel(pr[0][u]));
ucm[pr[0][u]]+=cm;
}
++vdt;
prq();
cout<<r.a[0][0]<<"\n";
}
void adq(in tx, long long ty){
mat crm;
crm.ini(3,1);
pair<fp,fp> tt=fbat(ty);
crm.a[0][0]=crm.a[1][0]=tt.first;
crm.a[2][0]=tt.second;
if(fid[tx]==-1){
fv[tx]+=crm;
return;
}
}
VI tpr;
VI cod,decod;
VVI tcd;
in nxdec;
void dfscod(in u){
forv(i,tcd[u]){
cod[nxdec]=tcd[u][i];
decod[tcd[u][i]]=nxdec;
++nxdec;
dfscod(tcd[u][i]);
}
}
void mkcod(){
in n=sz(tpr);
cod=decod=VI(n,-1);
tcd.resize(n);
for(in i=1;i<n;++i)
tcd[tpr[i]].PB(i);
cod[0]=decod[0]=0;
nxdec=1;
dfscod(0);
}
void mkt(){
in n,m;
cin>>n>>m;
lvs.resize(n,0);
vdt=1;
ucm.resize(n);
forn(i,n)
ucm[i].ini(3,3);
tpr.resize(n);
tpr[0]=0;
forn(i,n-1){
cin>>tpr[i+1];
--tpr[i+1];
}
mkcod();
forn(z,mxp)
pr[z].resize(n);
ht.resize(n);
fv.resize(n);
forn(i,n)
fv[i].ini(3,1);
ht[0]=0;
pr[0][0]=0;
forn(i,n-1){
pr[0][i+1]=decod[tpr[cod[i+1]]];
assert(pr[0][i+1]<i+1);
ht[i+1]=ht[pr[0][i+1]]+1;
}
for(in i=1;i<mxp;++i){
forn(j,n)
pr[i][j]=pr[i-1][pr[i-1][j]];
}
proct();
char typ;
in tx;
long long ty;
forn(zz,m){
cin>>typ>>tx>>ty;
if(typ=='Q'){
ansq(decod[tx-1],decod[ty-1]);
}
else{
}
}
}
const in mx=100009;
int main(){
ios::sync_with_stdio(0);
cin.tie(0);
smfib.ini(3,3);
smfib.a[0][0]=smfib.a[0][2]=smfib.a[1][2]=smfib.a[2][1]=smfib.a[2][2]=1;
sft.ini(3,1);
basfib.ini(2,1);
basfib.a[0][0]=basfib.a[1][0]=1LL;
fibmat.ini(2,2);
fibmat.a[0][0]=0;
fibmat.a[0][1]=fibmat.a[1][0]=fibmat.a[1][1]=1LL;
smpw.resize(mx);
smpw[0].ini(3,3);
forn(i,3)
smpw[0].a[i][i]=1;
for(in i=1;i<sz(smpw);++i)
smpw[i]=smpw[i-1]*smfib;
mkt();
return 0;
}

In   Java  :

import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class H {
InputStream is;
PrintWriter out;
String INPUT = "";

void solve(){
int n = ni();
int Q = ni();
par = new int[n];
for(int i = 1;i < n;i++){
par[i] = ni()-1;
}
par[0] = -1;
int[][] g = parentToG(par);
int[][] pars = parents3(g, 0);
int[] ord = pars[1], dep = pars[2];
clus = decomposeToHeavyLight(g,par, ord);
cluspath = clusPaths(clus, ord);
clusiind = clusIInd(cluspath, n);
int m = cluspath.length;
sts = new SegmentTreeMatrix[m];
for(int i = 0;i < m;i++){
sts[i] = new SegmentTreeMatrix(cluspath[i].length);
}
int[][] spar = logstepParents(par);

for(int z = 0;z < Q;z++){
char type = nc();
if(type == 'U'){
int x = ni()-1;
long K = nl();
sts[clus[x]].update(clusiind[x], K);
}else{
int mod = 1000000007;
int x = ni()-1, y = ni()-1;
int lca = lca2(x, y, spar, dep);
long ret = d(x)+d(y)-d(lca)-d(par[lca]);
ret %= mod;
if(ret < 0)ret += mod;
out.println(ret);
}
}
}

int[] par;
int[] clus, clusiind;
int[][] cluspath;
SegmentTreeMatrix[] sts;

long d(int x){
if(x == -1)return 0;
int[] lcx = new int[100];
int[] lto = new int[100];
int p = 0;
int cx = clus[x];
int ind = clusiind[x];
while (true) {
lcx[p] = cx;
lto[p] = ind+1;
p++;
int con = par[cluspath[cx][0]];
if(con == -1)break;
ind = clusiind[con];
cx = clus[con];
}
int[] v = {0, 0, 1, 0};
for(int i = p-1;i >= 0;i--){
v = sts[lcx[i]].apply(0, lto[i], v);
}
return v[3];
}

public static class SegmentTreeMatrix {
public int M, H, N;
public int[][][] node;
public static int mod = 1000000007;
public static long BIG = 8L*mod*mod;
public static int S = 4;

public SegmentTreeMatrix(int n){
N = n;
M = Integer.highestOneBit(Math.max(N-1, 1))<<2;
H = M>>>1;

node = new int[M][][];
for(int i = 0;i < N;i++){
node[H+i] = new int[S][S];
node[H+i][0][0] = 1;
node[H+i][0][1] = 1;
node[H+i][1][0] = 1;
node[H+i][3][1] = 1;
node[H+i][2][2] = 1;
node[H+i][3][3] = 1;
node[H+i][3][0] = 1;
}

for(int i = H-1;i >= 1;i--)propagate(i);
}

private void propagate(int cur){
node[cur] = prop2(node[2*cur], node[2*cur+1], node[cur]);
}

private int[][] prop2(int[][] L, int[][] R, int[][] C){
if(L != null && R != null){
C = mul(R, L, C, mod);
return C;
}else if(L != null){
return prop1(L, C);
}else if(R != null){
return prop1(R, C);
}else{
return null;
}
}

private int[][] prop1(int[][] L, int[][] C){
if(C == null){
C = new int[S][];
for(int i = 0;i < S;i++){
C[i] = Arrays.copyOf(L[i], S);
}
}else{
for(int i = 0;i < S;i++){
C[i] = Arrays.copyOf(L[i], S);
}
}
return C;
}

public void update(int pos, long x) {
int[][] M = {{1, 1}, {1, 0}};
int[] v = {1, 0};
v = pow(M, v, x-1);
node[H+pos][0][2] += v[0];
if(node[H+pos][0][2] >= mod)node[H+pos][0][2] -= mod;
node[H+pos][1][2] += v[1];
if(node[H+pos][1][2] >= mod)node[H+pos][1][2] -= mod;
node[H+pos][3][2] += v[0];
if(node[H+pos][3][2] >= mod)node[H+pos][3][2] -= mod;
for(int i = H+pos>>>1;i >= 1;i>>>=1)propagate(i);
}

public int[] apply(int l, int r, int[] v){
return apply(l, r, 0, H, 1, v);
}

if(l <= cl && cr <= r){
return mul(node[cur], v, mod);
}else{
int mid = cl+cr>>>1;
if(cl < r && l < mid){
v = apply(l, r, cl, mid, 2*cur, v);
}
if(mid < r && l < cr){
v = apply(l, r, mid, cr, 2*cur+1, v);
}
return v;
}
}

public static int[] mul(int[][] A, int[] v, int mod){
int m = A.length;
int n = v.length;
int[] w = new int[m];
for(int i = 0;i < m;i++){
long sum = 0;
for(int k = 0;k < n;k++){
sum += (long)A[i][k] * v[k];
if(sum >= BIG)sum -= BIG;
}
w[i] = (int)(sum % mod);
}
return w;
}

public static int[][]
mul(int[][] A, int[][] B, int[][] C, int mod){
int m = A.length;
int n = A[0].length;
int o = B[0].length;
if(C == null)C = new int[m][o];
for(int i = 0;i < m;i++){
for(int j = 0;j < o;j++){
long sum = 0;
for(int k = 0;k < n;k++){
sum += (long)A[i][k] * B[k][j];
if(sum >= BIG)sum -= BIG;
}
sum %= mod;
C[i][j] = (int)sum;
}
}
return C;
}

public static int[] pow(int[][] A, int[] v, long e){
for(int i = 0;i < v.length;i++){
if(v[i] >= mod)v[i] %= mod;
}
int[][] MUL = A;
for(;e > 0;e>>>=1) {
if((e&1)==1)v = mul(MUL, v);
MUL = p2(MUL);
}
return v;
}

public static int[] mul(int[][] A, int[] v){
int m = A.length;
int n = v.length;
int[] w = new int[m];
for(int i = 0;i < m;i++){
long sum = 0;
for(int k = 0;k < n;k++){
sum += (long)A[i][k] * v[k];
if(sum >= BIG)sum -= BIG;
}
w[i] = (int)(sum % mod);
}
return w;
}

public static int[][] p2(int[][] A){
int n = A.length;
int[][] C = new int[n][n];
for(int i = 0;i < n;i++){
long[] sum = new long[n];
for(int k = 0;k < n;k++){
for(int j = 0;j < n;j++){
sum[j] += (long)A[i][k] * A[k][j];
if(sum[j] >= BIG)sum[j] -= BIG;
}
}
for(int j = 0;j < n;j++){
C[i][j] = (int)(sum[j] % mod);
}
}
return C;
}

}

public static int lca2(int a, int b,
int[][] spar, int[] depth) {
if (depth[a] < depth[b]) {
b = ancestor(b, depth[b] - depth[a], spar);
} else if (depth[a] > depth[b]) {
a = ancestor(a, depth[a] - depth[b], spar);
}

if (a == b)
return a;
int sa = a, sb = b;
for (int low = 0, high = depth[a],
t = Integer.highestOneBit(high),
k = Integer.numberOfTrailingZeros(t); t > 0;
t >>>= 1, k--) {
if ((low ^ high) >= t) {
if (spar[k][sa] != spar[k][sb]) {
low |= t;
sa = spar[k][sa];
sb = spar[k][sb];
} else {
high = low | t - 1;
}
}
}
return spar[0][sa];
}

protected static int ancestor(int a, int m, int[][] spar) {
for (int i = 0; m > 0 && a != -1; m >>>= 1, i++) {
if ((m & 1) == 1)
a = spar[i][a];
}
return a;
}

public static int[][] logstepParents(int[] par) {
int n = par.length;
int m = Integer.numberOfTrailingZeros(
Integer.highestOneBit(n - 1)) + 1;
int[][] pars = new int[m][n];
pars[0] = par;
for (int j = 1; j < m; j++) {
for (int i = 0; i < n; i++) {
pars[j][i] = pars[j - 1][i] == -1 ? -1
: pars[j - 1][pars[j - 1][i]];
}
}
return pars;
}

public static int[]
decomposeToHeavyLight(int[][] g, int[] par, int[] ord) {
int n = g.length;
int[] size = new int[n];
Arrays.fill(size, 1);
for (int i = n - 1; i > 0; i--)
size[par[ord[i]]] += size[ord[i]];

int[] clus = new int[n];
Arrays.fill(clus, -1);
int p = 0;
outer: for (int i = 0; i < n; i++) {
int u = ord[i];
if (clus[u] == -1)
clus[u] = p++;
for (int v : g[u]) {
if (par[u] != v && size[v] >= size[u] / 2) {
clus[v] = clus[u];
continue outer;
}
}
for (int v : g[u]) {
if (par[u] != v) {
clus[v] = clus[u];
break;
}
}
}
return clus;
}

public static int[][] clusPaths(int[] clus, int[] ord) {
int n = clus.length;
int[] rp = new int[n];
int sup = 0;
for (int i = 0; i < n; i++) {
rp[clus[i]]++;
sup = Math.max(sup, clus[i]);
}
sup++;

int[][] row = new int[sup][];
for (int i = 0; i < sup; i++)
row[i] = new int[rp[i]];

for (int i = n - 1; i >= 0; i--) {
row[clus[ord[i]]][--rp[clus[ord[i]]]] = ord[i];
}
return row;
}

public static int[] clusIInd(int[][] clusPath, int n) {
int[] iind = new int[n];
for (int[] path : clusPath) {
for (int i = 0; i < path.length; i++) {
iind[path[i]] = i;
}
}
return iind;
}

public static int[][] parentToG(int[] par){
int n = par.length;
int[] ct = new int[n];
for(int i = 0;i < n;i++){
if(par[i] >= 0){
ct[i]++;
ct[par[i]]++;
}
}
int[][] g = new int[n][];
for(int i = 0;i < n;i++){
g[i] = new int[ct[i]];
}
for(int i = 0;i < n;i++){
if(par[i] >= 0){
g[par[i]][--ct[par[i]]] = i;
g[i][--ct[i]] = par[i];
}
}
return g;
}

public static int[][] parents3(int[][] g, int root) {
int n = g.length;
int[] par = new int[n];
Arrays.fill(par, -1);

int[] depth = new int[n];
depth[0] = 0;

int[] q = new int[n];
q[0] = root;
for (int p = 0, r = 1; p < r; p++) {
int cur = q[p];
for (int nex : g[cur]) {
if (par[cur] != nex) {
q[r++] = nex;
par[nex] = cur;
depth[nex] = depth[cur] + 1;
}
}
}
return new int[][] { par, q, depth };
}

static int[][] packU(int n, int[] from, int[] to) {
int[][] g = new int[n][];
int[] p = new int[n];
for (int f : from)
p[f]++;
for (int t : to)
p[t]++;
for (int i = 0; i < n; i++)
g[i] = new int[p[i]];
for (int i = 0; i < from.length; i++) {
g[from[i]][--p[from[i]]] = to[i];
g[to[i]][--p[to[i]]] = from[i];
}
return g;
}

void run() throws Exception{
is = INPUT.isEmpty() ?
System.in : new ByteArrayInputStream(INPUT.getBytes());
out = new PrintWriter(System.out);

long s = System.currentTimeMillis();
solve();
out.flush();
if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
}

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

private byte[] inbuf = new byte[1024];
private int lenbuf = 0, ptrbuf = 0;

if(lenbuf == -1)throw new InputMismatchException();
if(ptrbuf >= lenbuf){
ptrbuf = 0;
try { lenbuf = is.read(inbuf); }
catch (IOException e)
{ throw new InputMismatchException(); }
if(lenbuf <= 0)return -1;
}
return inbuf[ptrbuf++];
}

private boolean isSpaceChar(int c)
{ return !(c >= 33 && c <= 126); }
private int skip()
{ int b; while((b = readByte()) != -1
&& isSpaceChar(b)); return b; }

private double nd()
{ return Double.parseDouble(ns()); }
private char nc() { return (char)skip(); }

private String ns(){
int b = skip();
StringBuilder sb = new StringBuilder();
while(!(isSpaceChar(b))){
sb.appendCodePoint(b);
}
return sb.toString();
}

private char[] ns(int n){
char[] buf = new char[n];
int b = skip(), p = 0;
while(p < n && !(isSpaceChar(b))){
buf[p++] = (char)b;
}
return n == p ? buf : Arrays.copyOf(buf, p);
}

private char[][] nm(int n, int m){
char[][] map = new char[n][];
for(int i = 0;i < n;i++)map[i] = ns(m);
return map;
}

private int[] na(int n){
int[] a = new int[n];
for(int i = 0;i < n;i++)a[i] = ni();
return a;
}

private int ni(){
int num = 0, b;
boolean minus = false;
&& !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
}

while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
}
}

private long nl(){
long num = 0;
int b;
boolean minus = false;
&& !((b >= '0' && b <= '9') || b == '-'));
if(b == '-'){
minus = true;
}

while(true){
if(b >= '0' && b <= '9'){
num = num * 10 + (b - '0');
}else{
return minus ? -num : num;
}
}
}

private static void tr(Object... o)
{ System.out.println(Arrays.deepToString(o)); }
}

In   Python3  :

#!/usr/bin/python

mod = 10**9 + 7

cache = { 0: (0, 1), 1: (1, 1) }
def fib_pair(n):
if n in cache:
return cache[n]

hn = n//2
f, fp = fib_pair(hn)
if n&1:
res = (fp*fp + f*f) % mod, (2*f+fp)*fp % mod
else:
fm = fp - f
if fm < 0:
fm += mod
res = (2*fm+f)*f % mod, (fp*fp + f*f) % mod

if n < 1000000:
cache[n] = res

return res

n, m = map(int, input().strip().split())
parents = (n+1) * [0]
children = [[] for _ in range(n+1)]
for i in range(2, n+1):
j = int(input())
parents[i] = j
children[j].append(i)
depths = (n+1) * [0]
stack = [(1, 1)]
while stack:
i, d = stack.pop()
depths[i] = d
for j in children[i]:
stack.append((j, d+1))

nrs = (n+1) * [0]
for _ in range(m):
q, si, sj = input().strip().split()
if q == 'U':
x, k = int(si), int(sj)
fibs = list(fib_pair(k))
stack = [(x, 0)]
while stack:
y, l = stack.pop()
if l >= len(fibs):
fibs.append((fibs[-1] + fibs[-2]) % mod)
nrs[y] += fibs[l]
for z in children[y]:
stack.append((z, l+1))
else:
i, j = int(si), int(sj)
if depths[i] < depths[j]:
i, j = j, i
fsum = 0
while depths[j] < depths[i]:
fsum += nrs[i]
i = parents[i]
while i != j:
fsum += nrs[i] + nrs[j]
j = parents[j]
i = parents[i]
fsum += nrs[i]
print(fsum % mod)```
```

## Tree: Postorder Traversal

Complete the postorder function in the editor below. It received 1 parameter: a pointer to the root of a binary tree. It must print the values in the tree's postorder traversal as a single line of space-separated values. Input Format Our test code passes the root node of a binary tree to the postorder function. Constraints 1 <= Nodes in the tree <= 500 Output Format Print the

## Tree: Inorder Traversal

In this challenge, you are required to implement inorder traversal of a tree. Complete the inorder function in your editor below, which has 1 parameter: a pointer to the root of a binary tree. It must print the values in the tree's inorder traversal as a single line of space-separated values. Input Format Our hidden tester code passes the root node of a binary tree to your \$inOrder* func

## Tree: Height of a Binary Tree

The height of a binary tree is the number of edges between the tree's root and its furthest leaf. For example, the following binary tree is of height : image Function Description Complete the getHeight or height function in the editor. It must return the height of a binary tree as an integer. getHeight or height has the following parameter(s): root: a reference to the root of a binary

## Tree : Top View

Given a pointer to the root of a binary tree, print the top view of the binary tree. The tree as seen from the top the nodes, is called the top view of the tree. For example : 1 \ 2 \ 5 / \ 3 6 \ 4 Top View : 1 -> 2 -> 5 -> 6 Complete the function topView and print the resulting values on a single line separated by space.

## Tree: Level Order Traversal

Given a pointer to the root of a binary tree, you need to print the level order traversal of this tree. In level-order traversal, nodes are visited level by level from left to right. Complete the function levelOrder and print the values in a single line separated by a space. For example: 1 \ 2 \ 5 / \ 3 6 \ 4 F

## Binary Search Tree : Insertion

You are given a pointer to the root of a binary search tree and values to be inserted into the tree. Insert the values into their appropriate position in the binary search tree and return the root of the updated binary tree. You just have to complete the function. Input Format You are given a function, Node * insert (Node * root ,int data) { } Constraints No. of nodes in the tree <