#define _USE_MATH_DEFINES #include using namespace std; //template #define rep(i,a,b) for(int i=(a);i<(b);i++) #define rrep(i,a,b) for(int i=(a);i>(b);i--) #define ALL(v) (v).begin(),(v).end() typedef long long int ll; const int inf = 0x3fffffff; const ll INF = 0x3fffffffffffffff; template inline bool chmax(T& a,T b){ if(a inline bool chmin(T& a,T b){ if(a>b){a=b;return 1;}return 0; } //template end int mod=1e9+7; struct Mint { int val; Mint inv() const{ int tmp,a=val,b=mod,x=1,y=0; while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y); return Mint(x); } public: Mint():val(0){} Mint(ll x){if((val=x%mod)<0)val+=mod;} Mint pow(ll t){Mint res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;}return res;} Mint& operator+=(const Mint& x){if((val+=x.val)>=mod)val-=mod;return *this;} Mint& operator-=(const Mint& x){if((val+=mod-x.val)>=mod)val-=mod; return *this;} Mint& operator*=(const Mint& x){val=(ll)val*x.val%mod; return *this;} Mint& operator/=(const Mint& x){return *this*=x.inv();} Mint operator+(const Mint& x) const{return Mint(*this)+=x;} Mint operator-(const Mint& x) const{return Mint(*this)-=x;} Mint operator*(const Mint& x) const{return Mint(*this)*=x;} Mint operator/(const Mint& x) const{return Mint(*this)/=x;} }; struct factorial { vector Fact, Finv; public: factorial(int maxx){ Fact.resize(maxx+1),Finv.resize(maxx+1); Fact[0]=Mint(1); rep(i,0,maxx)Fact[i+1]=Fact[i]*(i+1); Finv[maxx]=Mint(1)/Fact[maxx]; rrep(i,maxx,0)Finv[i-1]=Finv[i]*i; } Mint fact(int n,bool inv=0){if(inv)return Finv[n];else return Fact[n];} Mint nPr(int n,int r){if(n<0||n