nCr%p in constant time.cpp

#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
typedef long long ll;
using namespace __gnu_pbds;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pbds;
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#define ios ios_base::sync_with_stdio(0) ; cin.tie(0) ; cout.tie(0)
#define so sizeof
#define pb push_back
#define cl clear() ;
#define vl vector<ll>
#define sz size()
#define len length()
#define el endl;cout.flush()
#define be begin()
#define fi first
#define se second
#define br break
#define en end()
#define ro return 0
#define br break
#define eb emplace_back
#define con continue
#define ms(x) memset(x , 0, so x)
#define all(x) (x).be , (x).en
#define rall(x) (x).rbegin() , (x).rend()
#define acc(x) accumulate((x).be , (x).en , 0ll)
#define forn(i,a,b) for(ll i=a;i<=b;++i)
#define rng_58 mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())
#define vll vector<pair<ll,ll> >
#define pll pair<ll,ll>
#define plll pair<ll,pair<ll,ll>>
#define plvl pair<pair<ll,ll> ,ll>
#define mp make_pair
#define trace2(a,b) cerr <<"a is " << a << " b is " << b << el;
#define trace3(a,b,c) cerr <<"a is " << a << " b is " << b << " c is " << c << el;
#define trace4(a,b,c,d) cerr <<"a is " << a << " b is " << b << " c is " << c <<" d is " << d << el ;
#define trace5(a,b,c,d,e) cerr <<"a is " << a << " b is " << b << " c is " << c <<" d is " << d << " e is " << e << el;
#define trace6(a,b,c,d,e,f) cerr <<"a is " << a << " b is " << b << " c is " << c <<" d is " << d << " e is " << e << " f is " << f << el ;
const ll p = 1e9+7 ;
const ll n = 1e6+1;
ll inv[n+2] , facinv[n+2] , fact[n+2] ;
void inverse()
{
    inv[0] = inv[1] = 1;
    forn(i , 2 , n){
       inv[i] = (inv[p%i]*(p-p/i))%p;
    }
}
void factinverse()
{
    facinv[0] = facinv[1] = 1 ;
    forn(i ,2 , n ){
       facinv[i] = (inv[i]*facinv[i-1])%p;
    }
}
void factorial()
{
    fact[0] = fact[1] = 1 ;
    forn(i , 2 , n ){
       fact[i] = (fact[i-1]*i)%p;
    }
}
ll ncr(ll N,ll R)
{
    ll res = ((fact[N] * facinv[R])%p * (facinv[N-R])) % p ;
    return res ;
}
int main()
{
    ios;
    inverse();
    factinverse();
    factorial();
    ll q;
    cin >>q ;
    forn(i ,1 , q){
      ll N,R;
      cin >> N>>R ;
      ll ans = ncr(N,R);
      cout << ans << el ;
    }
}