#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; typedef pair P; template inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } templatevoid Fill(A(&array)[N],const T &val){fill((T*)array, (T*)(array+N), val);} const int inf = INT_MAX / 2; const ll INF = LLONG_MAX / 2; //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) :val(x >= 0 ? x % mod : x % mod + mod) {} int mtoi() { return this->val; } 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(); } bool operator==(const Mint& x) const { return val == x.val; } bool operator!=(const Mint& x) const { return val != x.val; } bool operator<(const Mint& x) const { return val < x.val; } bool operator<=(const Mint& x) const { return val <= x.val; } bool operator>(const Mint& x) const { return val > x.val; } bool operator>=(const Mint& x) const { return val >= x.val; } 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,Mint(1)),Finv.resize(maxx+1); rep(i,0,maxx)Fact[i+1]=Fact[i]*Mint(i+1); Finv[maxx]=Mint(1)/Fact[maxx]; rrep(i,maxx,0)Finv[i-1]=Finv[i]*Mint(i); } Mint fact(int n,bool inv) { if(inv) return Finv[n]; else return Fact[n]; } Mint nPr(int n,int r) { if(n<0||n