#embrace <bits/stdc++.h>
utilizing namespace std;
#outline ll lengthy lengthy
class Resolution {
public:
int nCrModM(int n, int r, int p)
{
vector<int> primes = findPrimeFactors(p);
vector<int> rem;
for (auto m : primes)
rem.push_back(Lucas(n, r, m));
int min_x = 0;
whereas (true) {
bool discovered = true;
for (int i = 0; i < primes.measurement();
i++) {
if (min_x % primes[i] != rem[i]) {
discovered = false;
break;
}
}
if (discovered) {
return min_x;
}
min_x++;
}
return min_x;
}
int Lucas(int n, int r, int m)
{
if (r == 0)
return 1;
int ni = n % m;
int ri = r % m;
return (pascal(ni, ri, m)
* Lucas(n / m, r / m, m))
% m;
}
ll pascal(int n, int r, int m)
{
if (r == 0 or r == n)
return 1;
int nCr[r + 1];
memset(nCr, 0, sizeof(nCr));
nCr[0] = 1;
for (int i = 1; i <= n; i++) {
for (int j = min(r, i); j > 0; j--)
nCr[j]
= (nCr[j] + nCr[j - 1]) % m;
}
return nCr[r];
}
vector<int> findPrimeFactors(int n)
{
vector<int> primes;
if (n % 2 == 0) {
primes.push_back(2);
whereas (n % 2 == 0)
n >>= 1;
}
for (int i = 3; n > 1; i += 2) {
if (n % i == 0) {
primes.push_back(i);
whereas (n % i == 0)
n /= i;
}
}
return primes;
}
};
int most important()
{
int n = 10, r = 2, p = 13;
Resolution obj;
int ans = obj.nCrModM(n, r, p);
cout << ans;
return 0;
}
