NcK.cpp

#include <bits/stdc++.h>
using namespace std;

#pragma GCC target   ("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx")
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("-ffloat-store")
#pragma GCC optimize ("Ofast")

static auto _ = [] () {
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cout.tie(nullptr);
    return 0;
}();

#define frw(i, len) for(ll i = 0   ; i < len ; i++)
#define frb(i, len) for(ll i = len ; i >= 0  ; i--)

#define YES cout<<"Yes \n";
#define NOO cout<<"No  \n";
#define nl cout<<"\n";

#define MAX_SIZE 10000
#define nptr nullptr

typedef stringstream strgm;
typedef long long int ll;
typedef const int c_int;
typedef unsigned unsg;
typedef double dbl;

typedef vector<vector<string>> vvstr;
typedef vector<vector<bool>> vvbl;
typedef vector<vector<int>> vvint;
typedef vector<vector<ll>> vvll;

typedef vector<string> vstr;
typedef vector<int> vint;
typedef vector<bool> vbl;
typedef vector<ll> vll;

typedef stack<string> sstr;
typedef stack<bool> sbl;
typedef stack<int> sint;
typedef stack<ll> sll;

typedef queue<string> qstr;
typedef queue<bool> qbl;
typedef queue<int> qint;
typedef queue<ll> qll;

c_int MOD=1e9 + 7;
c_int Mx_row=100;
c_int Mx_col=100;
int size_stack=0;
int InvrsnCnt=0;
int size_arr=0;
int size_ll=0;
int top=-1;

c_int MOD = 1e9 + 7;
c_int N = 1e5 + 10;
c_int MAXN = 1e5 + 10;
vint Fact(N, 1);

int BinExpo(int a, int b, int m) {
    int res = 1;
    while (b > 0) {
        if (b & 1) {
            res = (res * 1LL * a) % m;
        }
        a = (a * 1LL * a) % m;
        b >>= 1;
    }
    return res;
}

int main() {
    for (int i = 1; i < MAXN; i++) {
        Fact[i] = (i * 1LL * Fact[i-1]) % MOD;
    }
    int q; 
    cin >> q;
    while (q--) {
        int n; 
        cin >> n;
        int k; 
        cin >> k;
        if (n < k) {
            cout << 0 << "\n"; 
            continue;
        }
        int ans = Fact[n] * ((ans * 1ll * Fact[k])%MOD);
        int den = (Fact[n-k] * 1LL * Fact[k]) % MOD;
        ans = (ans * 1LL * BinExpo(den, MOD-2, MOD)) % MOD;
        cout << ans << "\n";
    }
    return 0;
}