#include #define rep(i,n) for(int i=0;i<(int)(n);i++) #define chmin(x,y) x = min((x),(y)); #define chmax(x,y) x = max((x),(y)); using namespace std; using ll = long long ; using P = pair ; using pll = pair; const int INF = 1e9; const long long LINF = 1e17; const int MOD = 1000000007; //const int MOD = 998244353; const double PI = 3.14159265358979323846; template struct ModInt{ long long x=0; constexpr ModInt(long long x=0):x((x%mod+mod)%mod){} constexpr ModInt operator+(const ModInt& r)const{return ModInt(*this)+=r;} constexpr ModInt operator-(const ModInt& r)const{return ModInt(*this)-=r;} constexpr ModInt operator*(const ModInt& r)const{return ModInt(*this)*=r;} constexpr ModInt operator/(const ModInt& r)const{return ModInt(*this)/=r;} constexpr ModInt& operator+=(const ModInt& r){ if((x+=r.x)>=mod) x-=mod; return *this;} constexpr ModInt& operator-=(const ModInt& r){ if((x-=r.x)<0) x+=mod; return *this;} constexpr ModInt& operator*=(const ModInt& r){ if((x*=r.x)>=mod) x%=mod; return *this;} constexpr ModInt& operator/=(const ModInt& r){ return *this*=r.inv();} constexpr bool operator==(const ModInt& r){ return x == r.x;} constexpr bool operator!=(const ModInt& r){ return x != r.x;} ModInt inv() const { long long s=x,sx=1,sy=0,t=mod,tx=0,ty=1; while(s%t!=0){ long long temp=s/t,u=s-t*temp,ux=sx-temp*tx,uy=sy-temp*ty; s=t;sx=tx;sy=ty; t=u;tx=ux;ty=uy; } return ModInt(tx); } ModInt pow(long long n) const { ModInt a=1; ModInt b=*this; while(n>0){ if(n&1) a*=b; b*=b; n>>=1; } return a; } friend constexpr ostream& operator<<(ostream& os,const ModInt& a) {return os << a.x;} friend constexpr istream& operator>>(istream& is,ModInt& a) {return is >> a.x;} }; using mint = ModInt; struct combination{ int N; vector fac,finv,inverse; combination(int N):N(N){ fac.resize(N+1);finv.resize(N+1); fac[0]=1; for(int i=1;i<=N;++i){fac[i]=fac[i-1]*i;} finv[N]=fac[N].inv(); for(int i=N-1;i>=0;--i){finv[i]=finv[i+1]*(i+1);} } void inverse_build(){ inverse.resize(N+1); inverse[1]=1; for(int i=2;i<=N;++i){inverse[i]=finv[i]*fac[i-1];} } mint c(int n,int k){ if(n> n; vector b(n); rep(i,n) cin >> b[i]; mint ans = 1; int sum = 0; int c = 0; for(int i=0;i