**Problem Link**: https://atcoder.jp/contests/tdpc/tasks/tdpc_dice

**How I Solved the Problem**: First of all I factored the number D as a product of primes 2, 3, 5 by storing the number of times each prime appears. If D has a prime factor other than 2,3,5 then the required probability will be 0. Otherwise there might exist some non-zero probability. For that I came up with the following recurrence.

prob(n,i,j,k) = (prob(n-1,i,j,k) + prob(n-1,i+1,j,k) + prob(n-1,i,j+1,k) + prob(n-1,i+2,j,k) + prob(n-1,i,j,k+1) + prob(n-1,i+1,j+1,k))/6. Here p(n,i,j,k) is the probability of getting a multiple of D when I have n throws remaining, with i 2’s, j 3’s, k 5’s accumulated till now.

**My Code**:

```
#include <bits/stdc++.h>
using namespace std;
#define FASTIO ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
using ll = long long;
using lld = long double;
const int MOD = 1e9+7;
const ll INF = 1e18;
int num;
ll d;
int cnt2 = 0, cnt3 = 0, cnt5 = 0;
void factor(int p, int& cnt) {
while(d%p == 0) {
cnt++;
d /= p;
}
}
lld dp[105][65][40][30];
lld prob(int n, int i, int j, int k) {
if(n == 0 && i >= cnt2 && j >= cnt3 && k >= cnt5) return dp[n][i][j][k] = 1;
if(n == 0 && (i <= cnt2 || j <= cnt3 || k <= cnt5)) return dp[n][i][j][k] = 0;
if(dp[n][i][j][k] != -1) return dp[n][i][j][k];
dp[n][i][j][k] = (prob(n-1,i,j,k) + prob(n-1,i+1,j,k) + prob(n-1,i,j+1,k)
+ prob(n-1,i+2,j,k) + prob(n-1,i,j,k+1) + prob(n-1,i+1,j+1,k))/6;
return dp[n][i][j][k];
}
int main() {
FASTIO
cin >> num >> d;
factor(2,cnt2); factor(3,cnt3); factor(5,cnt5);
if(d != 1) {
cout << 0 << "\n";
}
else {
for(int n=0; n<105; n++) {
for(int i=0; i<65; i++) {
for(int j=0; j<40; j++) {
for(int k=0; k<30; k++) {
dp[n][i][j][k] = -1;
}
}
}
}
cout << fixed << setprecision(6) << prob(num,0,0,0) << "\n";
}
return 0;
}
```

I have tried this code on the sample test cases and I am getting the correct answers but still the code gives a WA on submission. I tried looking for a similar problem (with the solution) but couldn’t find any. So I don’t know what is wrong with the logic or the implementation. Can anyone please help?