#include // ver2.7.1 #define int long long #define endl "\n" // fflush(stdout); #define ALL(v) (v).begin(),(v).end() #define Vi vector #define VVi vector #define VVVi vector #define Vm vector #define Vs vector #define Vd vector #define Vc vector #define Pii pair #define Pdd pair #define VPii vector #define Tiii tuple #define VTiii vector #define PQi priority_queue #define PQir priority_queue,greater> #define pb push_back #define mp make_pair #define mt make_tuple #define itos to_string #define stoi stoll #define FI first #define SE second #define cYES cout<<"YES"<()) #define rep(i,a,b) for(int i=a;i=b;i--) #define dem(a,b) ((a+b-1)/(b)) #define INF 3000000000000000000 // 3.0*10^18 #define MAX LLONG_MAX #define PI acos(-1.0L) //int MOD = 998244353; // case const int MOD = 1000000007; // 10^9 + 7 const double EPS = 1e-10; using namespace std; struct mint{int x;mint(int x=0):x((x%MOD+MOD)%MOD){} mint operator-()const{return mint(-x);} mint& operator+=(const mint a){if((x+=a.x)>=MOD)x-=MOD;return*this;} mint& operator-=(const mint a){if((x+=MOD-a.x)>=MOD)x-=MOD;return*this;} mint& operator*=(const mint a){(x*=a.x)%=MOD;return*this;} mint operator+(const mint a)const{return mint(*this)+=a;} mint operator-(const mint a)const{return mint(*this)-=a;} mint operator*(const mint a)const{return mint(*this)*=a;} mint pow(int t)const{if(!t)return 1;mint a=pow(t>>1);a*=a;if(t&1)a*=*this;return a;} mint inv()const{return pow(MOD-2);} mint& operator/=(const mint a){return*this*=a.inv();} mint operator/(const mint a)const{return mint(*this)/=a;}}; istream& operator>>(istream& is, const mint& a) {return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) {return os << a.x;} /* debug */ template // vector ostream& operator<<(ostream& os,const vector &V){int N=V.size(); if(N==0){os<<'.';return os;}rep(i,0,N-1){os< // vector vector ostream& operator<<(ostream& os,const vector> &V){ int N=V.size();rep(i,0,N-1)cout< // pair ostream& operator<<(ostream& os, pair const&P){os< // set ostream& operator<<(ostream& os,set &S){auto it=S.begin();while(it!=S.end()){ os<<*it;if(next(it,1)!=S.end())os<<' ';it++;};return os;} template // deque ostream& operator<<(ostream& os, deque &q){for(auto it=q.begin();itvoid Vin(vector &v){int n=v.size();rep(i,0,n)cin>>v[i];} int gcd(int a,int b){return b?gcd(b,a%b):a;} int lcm(int a,int b){return a/gcd(a,b)*b;} int mypow(int x, int n, int m){ if(n==0)return 1;if(n%2==0)return mypow(x*x%m,n/2,m);else return x*mypow(x,n-1,m)%m;} int scomb(int n, int r){if(r<0||r>n)return 0;if((n-r)n-r;--i){a=a*i;}for(int i=1;i0){ret+=n%10;n/=10;}return ret;} int digit(int k,int i){string s = itos(k);return s[s.size()-i]-'0';} // i桁目の数字 templatevoid press(T &v){v.erase(unique(ALL(v)),v.end());} // 圧縮 Vi zip(Vi b){int Z=b.size(); // 座標圧縮 Pii p[Z+10];int a=b.size();Vi l(a);for(int i=0;i