#include typedef uint64_t u64; typedef int64_t i64; typedef long double f128; using namespace std; void scan(){} template void scan(T& n,Args&... args){ cin>>n; scan(args...); } template void scanall(T start,T end){ for(;start!=end;++start){ scan(*start); } } void print(){} template void print(T n,Args... args){ cout< void println(T n){ cout< void println(T n,Args... args){ cout< void printall(T start,T end){ if(start!=end){ cout<<(*start); for(++start;start!=end;++start){ cout<<' '<<(*start); } } cout< void chmax(T& n,T m){ n=max(n,m); } template void chmin(T& n,T m){ n=min(n,m); } template T power(T a,U n){ T res=1; while(n){ res*=((n&1)?a:1); a*=a; n>>=1; } return res; } i64 power(i64 a,i64 n,i64 m){ i64 res=1%m; while(n){ if(n&1){ res=res*a%m; } a=a*a%m; n>>=1; } return res; } template struct combination{ vector fact,fact_inv; combination(int mx=3000000):fact(mx+1,1),fact_inv(mx+1,1){ for(int i=2;i<=mx;++i){ fact[i]=fact[i-1]*i; } fact_inv[mx]/=fact[mx]; for(int i=mx;i>0;--i){ fact_inv[i-1]=fact_inv[i]*i; } } template T nCk(U n,U k){ if(n struct modint{ u64 val; constexpr modint(const i64 x=0) noexcept:val((x%i64(mod)+i64(mod))%i64(mod)){} constexpr modint operator+(const modint rhs) const noexcept{ return modint(*this)+=rhs; } constexpr modint operator-(const modint rhs) const noexcept{ return modint(*this)-=rhs; } constexpr modint operator*(const modint rhs) const noexcept{ return modint(*this)*=rhs; } constexpr modint operator/(const modint rhs) const noexcept{ return modint(*this)/=rhs; } constexpr modint &operator+=(const modint rhs) noexcept{ val+=rhs.val; val-=((val>=mod)?mod:0); return *this; } constexpr modint &operator-=(const modint rhs) noexcept{ val+=((val>=1; } return *this; } friend constexpr ostream &operator<<(ostream &os,const modint &x) noexcept{ return os<<(x.val); } friend constexpr istream &operator>>(istream &is,modint &x) noexcept{ u64 t; is>>t; x=t; return is; } }; template void dft(vector>& f,int inverse){ constexpr modint g=3; typedef modint mint; i64 siz=f.size(); if(siz==1){ return; } vector fl(siz/2),fr(siz/2); for(int i=0;i vector> mul_NTTfriendlyprime(vector> a,vector> b){ int siz=1,mxsiz=a.size()+b.size()-1; while(siz ext_gcd(i64 a,i64 b){ if(b==0){ return {1,0}; } i64 r=a%b; i64 x=ext_gcd(b,r).second; i64 y=(1-a*x)/b; return {x,y}; } i64 inv_mod(i64 a,i64 m){ assert(gcd(a,m)==1); return (ext_gcd(a,m).first+m)%m; } i64 garner(vector r,vector m,u64 mod){ int siz=m.size(); m.emplace_back(mod); vector m_prod(siz+1); vector x(siz+1); for(int i=0;i mul_anymod(vector a,vector b,u64 mod){ constexpr u64 mod0=998244353,mod1=167772161,mod2=469762049; vector> a0(a.size()),b0(b.size()); vector> a1(a.size()),b1(b.size()); vector> a2(a.size()),b2(b.size()); for(size_t i=0;i> c0=mul_NTTfriendlyprime(a0,b0); vector> c1=mul_NTTfriendlyprime(a1,b1); vector> c2=mul_NTTfriendlyprime(a2,b2); vector res(a.size()+b.size()-1); for(size_t i=0;i>> prime_fact(int n,int m){ vector>> res; for(int i=2;i*i<=n;++i){ if(n%i!=0){ continue; } int now=1; while(n%i==0){ n/=i; now*=i; } res.push_back({i,{now,m%now}}); } if(n!=1){ res.push_back({n,{n,m%n}}); } return res; } void solve(){ constexpr i64 mod=1000000007; int N; scan(N); vector X(N),Y(N); for(int i=0;i>> mp; for(int i=0;i x,y; for(auto& [a,b]:mp){ sort(b.rbegin(),b.rend()); for(size_t i=0;i