#include using namespace std; using Int = long long; template inline void chmin(T1 &a,T2 b){if(a>b) a=b;} template inline void chmax(T1 &a,T2 b){if(a struct Mint{ static constexpr T mod = MOD; T v; Mint():v(0){} Mint(signed v):v(v){} Mint(long long t){v=t%MOD;if(v<0) v+=MOD;} Mint pow(long long k){ Mint res(1),tmp(v); while(k){ if(k&1) res*=tmp; tmp*=tmp; k>>=1; } return res; } static Mint add_identity(){return Mint(0);} static Mint mul_identity(){return Mint(1);} Mint inv(){return pow(MOD-2);} Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;} Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;} Mint& operator/=(Mint a){return (*this)*=a.inv();} Mint operator+(Mint a) const{return Mint(v)+=a;}; Mint operator-(Mint a) const{return Mint(v)-=a;}; Mint operator*(Mint a) const{return Mint(v)*=a;}; Mint operator/(Mint a) const{return Mint(v)/=a;}; Mint operator-() const{return v?Mint(MOD-v):Mint(v);} bool operator==(const Mint a)const{return v==a.v;} bool operator!=(const Mint a)const{return v!=a.v;} bool operator <(const Mint a)const{return v dp; dp.reserve(sq); Mint res(1); for(Int r=0;r0) return idx; } res*=p; } assert(0); return T(-1); } static Mint comb(long long n,Int k){ Mint num(1),dom(1); for(Int i=0;i constexpr T Mint::mod; template ostream& operator<<(ostream &os,Mint m){os< class Enumeration{ private: static vector fact,finv,invs; public: static void init(Int n){ n=min(n,M::mod-1); Int m=fact.size(); if(n=m;i--) finv[i-1]=finv[i]*M(i); for(Int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1]; } static M Fact(Int n){ init(n); return fact[n]; } static M Finv(Int n){ init(n); return finv[n]; } static M Invs(Int n){ init(n); return invs[n]; } static M C(Int n,Int k){ if(n > D(Int n,Int m){ vector > dp(n+1,vector(m+1,0)); dp[0][0]=M(1); for(Int i=0;i<=n;i++){ for(Int j=1;j<=m;j++){ if(i-j>=0) dp[i][j]=dp[i][j-1]+dp[i-j][j]; else dp[i][j]=dp[i][j-1]; } } return dp; } static M B(Int n,Int k){ if(n==0) return M(1); k=min(k,n); init(k); vector dp(k+1); dp[0]=M(1); for(Int i=1;i<=k;i++) dp[i]=dp[i-1]+((i&1)?-finv[i]:finv[i]); M res; for(Int i=1;i<=k;i++) res+=M(i).pow(n)*finv[i]*dp[k-i]; return res; } static M montmort(Int n){ M res; init(n); for(Int k=2;k<=n;k++){ if(k&1) res-=finv[k]; else res+=finv[k]; } return res*=fact[n]; } static M LagrangePolynomial(vector &y,M t){ Int n=y.size()-1; if(t.v<=n) return y[t.v]; init(n+1); vector dp(n+1,1),pd(n+1,1); for(Int i=0;i0;i--) pd[i-1]=pd[i]*(t-M(i)); M res{0}; for(Int i=0;i<=n;i++){ M tmp=y[i]*dp[i]*pd[i]*finv[i]*finv[n-i]; if((n-i)&1) res-=tmp; else res+=tmp; } return res; } }; template vector Enumeration::fact = vector(); template vector Enumeration::finv = vector(); template vector Enumeration::invs = vector(); //INSERT ABOVE HERE signed main(){ Int n,k; cin>>n>>k; using M = Mint; using E = Enumeration; M ans{0}; vector dp(n+1,0); vector cand; for(Int i=1;i