#include "bits/stdc++.h" #define REP(i,num) for(ll i=0;i<(num);++i) #define FOR(i,c,num) for(ll (i)=(c);(i)<(num);++(i)) #define LOOP(i) while(i--) #define ALL(c) c.begin(),c.end() #define PRINTALL(c) for(auto pitr=c.begin();pitr!=c.end();++pitr){cout<<*pitr;if(next(pitr,1)!=c.end())cout<<' ';}cout<& lhs,const pair& rhs){return lhs.c comp rhs.c;} using namespace std; using ll = long long; using vll = vector; using vvll = vector>; constexpr ll atcoder_mod = 1e9+7; template T in(){ T x; cin >> x; return (x); } template> C vecin(int N){ C x(N);REP(i,N){ x[i]=in(); }return x; } void vout(){ cout << endl; } template void vout(Head&& h,Tail&&... t){ cout << ' ' << h;vout(forward(t)...); } void out(){ cout << endl; } template void out(Head&& h,Tail&&... t){ cout << h;vout(forward(t)...); } template bool chmax(T& a,T b){ if(a bool chmin(T& a,T b){ if(a>b){ a=b;return true; }return false; } class Combination{ constexpr static int atcoder_mod = 1000000007; vector fac,finv,inv; public: Combination(ll N){ fac.resize(N+1); finv.resize(N+1); inv.resize(N+1); fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for(int i=2;i<=N;i++){ fac[i] = fac[i-1] * i % atcoder_mod; inv[i] = atcoder_mod - inv[atcoder_mod%i] * (atcoder_mod/i) % atcoder_mod; finv[i] = finv[i-1] * inv[i] % atcoder_mod; } } ll Caluclation(ll n,ll r){ if(n < r) return 0; if (n < 0 || r < 0) return 0; return fac[n] * (finv[r] * finv[n-r] % atcoder_mod) % atcoder_mod; } ll GetFInv(ll i){ return finv[i]; } }; int main(){ cin.tie(0); ios::sync_with_stdio(false); cout<