**Bit Array**

### Problem Statement :

You are given four integers: N ,S ,P ,Q . You will use them in order to create the sequence a with the following pseudo-code. a[0] = S (modulo 2^31) for i = 1 to N-1 a[i] = a[i-1]*P+Q (modulo 2^31) Your task is to calculate the number of distinct integers in the sequence a. Input Format Four space separated integers on a single line N,S ,P and Q respectively. Output Format A single integer that denotes the number of distinct integers in the sequence a . Constraints 1 <= N <= 10^8 0 <= S,P,Q <= 2^31

### Solution :

` ````
Solution in C :
#include <cmath>
#include <cstdio>
#include <vector>
#include <iostream>
#include <algorithm>
using namespace std;
unsigned long long mask[40000000];
unsigned insert(unsigned x) {
unsigned res = (mask[x >> 6] & (1ULL << (x & 0x3F))) == 0;
mask[x >> 6] |= 1ULL << (x & 0x3F);
return res;
}
int main() {
unsigned N, S, P, Q;
cin >> N >> S >> P >> Q;
unsigned x = S;
unsigned ans = 0;
ans += insert(x);
for (unsigned i = 1; i < N; i++) {
x = (1LL * x * P + Q) % 2147483648;
ans += insert(x);
}
cout << ans << endl;
return 0;
}
```

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