ncr mod k

// A modular inverse based solution to 
// compute nCr % p 
#include <bits/stdc++.h> 
using namespace std; 
  
/* Iterative Function to calculate (x^y)%p  
in O(log y) */
unsigned long long power(unsigned long long x, 
                         int y, int p) 
{ 
    unsigned long long res = 1; // Initialize result 
  
    x = x % p; // Update x if it is more than or 
    // equal to p 
  
    while (y > 0) { 
        // If y is odd, multiply x with result 
        if (y & 1) 
            res = (res * x) % p; 
  
        // y must be even now 
        y = y >> 1; // y = y/2 
        x = (x * x) % p; 
    } 
    return res; 
} 
  
// Returns n^(-1) mod p 
unsigned long long modInverse(unsigned long long n, int p) 
{ 
    return power(n, p - 2, p); 
} 
  
// Returns nCr % p using Fermat's little 
// theorem. 
unsigned long long nCrModPFermat(unsigned long long n, 
                                 int r, int p) 
{ 
    // Base case 
    if (r == 0) 
        return 1; 
  
    // Fill factorial array so that we 
    // can find all factorial of r, n 
    // and n-r 
    unsigned long long fac[n + 1]; 
    fac[0] = 1; 
    for (int i = 1; i <= n; i++) 
        fac[i] = (fac[i - 1] * i) % p; 
  
    return (fac[n] * modInverse(fac[r], p) % p * modInverse(fac[n - r], p) % p) % p; 
} 
  
// Driver program 
int main() 
{ 
    // p must be a prime greater than n. 
    int n = 10, r = 2, p = 13; 
    cout << "Value of nCr % p is "
         << nCrModPFermat(n, r, p); 
    return 0; 
}