#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 NTT{ static constexpr int md = bmds(X); static constexpr int rt = brts(X); inline int add(int a,int b){ a+=b; if(a>=md) a-=md; return a; } inline int mul(int a,int b){ return 1LL*a*b%md; } inline int pow(int a,int b){ int res=1; while(b){ if(b&1) res=mul(res,a); a=mul(a,a); b>>=1; } return res; } inline int inv(int x){ return pow(x,md-2); } vector > rts,rrts; void ensure_base(int n){ if((int)rts.size()>=n) return; rts.resize(n);rrts.resize(n); for(int i=1;i &a,bool f,int n=-1){ if(n==-1) n=a.size(); assert((n&(n-1))==0); for(int i=0,j=1;j+1>1;k>(i^=k);k>>=1); if(i>j) swap(a[i],a[j]); } for(int i=1;i multiply(vector &a,vector &b){ int need=a.size()+b.size()-1; int sz=1; while(sz f(sz),g(sz); for(int i=0;i<(int)a.size();i++) f[i]=a[i]; for(int i=0;i<(int)b.size();i++) g[i]=b[i]; ntt(f,0);ntt(g,0); for(int i=0;i struct ArbitraryModConvolution{ using ll = long long; NTT<0> ntt0; NTT<1> ntt1; NTT<2> ntt2; void garner(vector< vector > &cs){ size_t sz=cs[0].size(); const int r01=ntt1.inv(ntt0.md); const int r02=ntt2.inv(ntt0.md); const int r12=ntt2.inv(ntt1.md); const int m01 =(ll)ntt0.md*ntt1.md%MOD; for(size_t i=0;i=MOD) cs[0][i]-=MOD; cs[0][i]+=(ll)cs[2][i]*m01%MOD; if(cs[0][i]>=MOD) cs[0][i]-=MOD; } } vector multiply(vector a, vector b) { for(int& x:a) x%=MOD; for(int& x:b) x%=MOD; vector< vector > cs(3); cs[0]=ntt0.multiply(a,b); cs[1]=ntt1.multiply(a,b); cs[2]=ntt2.multiply(a,b); size_t sz=a.size()+b.size()-1; for(auto& v:cs) v.resize(sz); garner(cs); return cs[0]; } }; //END CUT HERE template struct Mint{ 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 fact,finv,invs; static void init(int n){ int m=fact.size(); if(n=m;i--) finv[i-1]=finv[i]*Mint(i); for(int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1]; } static Mint C(int n,int k){ if(n vector > Mint::fact = vector >(); template vector > Mint::finv = vector >(); template vector > Mint::invs = vector >(); //INSERT ABOVE HERE signed YUKI_829(){ using ll = long long; int n,b; cin>>n>>b; vector s(n); for(Int i=0;i>s[i]; using M = Mint; M::init(3e5); vector cnt(n,0); for(int i=0;i > ; priority_queue

pq; pq.emplace(-1,vector(1,1)); int sum=0; for(int i=n-1;i>=0;i--){ if(cnt[i]==0) continue; M x=M::H(sum,cnt[i]); M y=M::H(sum+1,cnt[i])-x; x*=M::fact[cnt[i]]; y*=M::fact[cnt[i]]; pq.emplace(-2,vector({x.v,y.v})); sum+=cnt[i]; } const int MOD = 1e9+7; ArbitraryModConvolution arb; while(pq.size()>1u){ auto a=pq.top().second;pq.pop(); auto b=pq.top().second;pq.pop(); auto c=arb.multiply(a,b); pq.emplace(-(int)c.size(),c); } auto dp=pq.top().second; M ans(0),res(1); for(int j=0;j<(int)dp.size();j++){ ans+=M((ll)j*(ll)dp[j])*res; res*=M(b); } cout<