#include #define For(i, a, b) for(int (i)=(int)(a); (i)<(int)(b); ++(i)) #define rFor(i, a, b) for(int (i)=(int)(a)-1; (i)>=(int)(b); --(i)) #define rep(i, n) For((i), 0, (n)) #define rrep(i, n) rFor((i), (n), 0) #define fi first #define se second using namespace std; typedef long long lint; typedef unsigned long long ulint; typedef pair pii; typedef pair pll; template bool chmax(T &a, const T &b){if(a bool chmin(T &a, const T &b){if(a>b){a=b; return true;} return false;} template T div_floor(T a, T b){ if(b < 0) a *= -1, b *= -1; return a>=0 ? a/b : (a+1)/b-1; } template T div_ceil(T a, T b){ if(b < 0) a *= -1, b *= -1; return a>0 ? (a-1)/b+1 : a/b; } constexpr lint mod = 1e9+7; constexpr lint INF = mod * mod; constexpr int MAX = 200010; template struct modint{ using i64=int_fast64_t; i64 a; modint(const i64 a_=0): a(a_){ if(a>MOD) a%=MOD; else if(a<0) (a%=MOD)+=MOD; } modint inv(){ i64 t=1, n=MOD-2, x=a; while(n){ if(n&1) (t*=x)%=MOD; (x*=x)%=MOD; n>>=1; } modint ret(t); return ret; } bool operator==(const modint x) const{return a==x.a;} bool operator!=(const modint x) const{return a!=x.a;} modint operator+(const modint x) const{ return modint(*this)+=x; } modint operator-(const modint x) const{ return modint(*this)-=x; } modint operator*(const modint x) const{ return modint(*this)*=x; } modint operator/(const modint x) const{ return modint(*this)/=x; } modint operator^(const lint x) const{ return modint(*this)^=x; } modint &operator+=(const modint &x){ a+=x.a; if(a>=MOD) a-=MOD; return *this; } modint &operator-=(const modint &x){ a-=x.a; if(a<0) a+=MOD; return *this; } modint &operator*=(const modint &x){ (a*=x.a)%=MOD; return *this; } modint &operator/=(modint x){ (a*=x.inv().a)%=MOD; return *this; } modint &operator^=(lint n){ i64 ret=1; while(n){ if(n&1) (ret*=a)%=MOD; (a*=a)%=MOD; n>>=1; } a=ret; return *this; } modint operator-() const{ return modint(0)-*this; } modint &operator++(){ return *this+=1; } modint &operator--(){ return *this-=1; } bool operator<(const modint x) const{ return a; vector fact; vector revfact; void setfact(int n){ fact.resize(n+1); revfact.resize(n+1); fact[0] = 1; rep(i, n) fact[i+1] = fact[i] * mint(i+1); revfact[n] = fact[n].inv(); for(int i=n-1; i>=0; i--) revfact[i] = revfact[i+1] * mint(i+1); } mint getC(int n, int r){ if(n