#include #define all(v) v.begin(), v.end() #define rall(v) v.rbegin(), v.rend() #define rep(i,n) for (int i=0;i<(int)(n);i++) #define codefor int test;scanf("%d",&test);while(test--) #define INT(...) int __VA_ARGS__;in(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;in(__VA_ARGS__) #define yes(ans) if(ans)printf("yes\n");else printf("no\n") #define Yes(ans) if(ans)printf("Yes\n");else printf("No\n") #define YES(ans) if(ans)printf("YES\n");else printf("NO\n") #define vector1d(type,name,...) vectorname(__VA_ARGS__) #define vector2d(type,name,h,...) vector>name(h,vector(__VA_ARGS__)) #define umap unordered_map #define uset unordered_set using namespace std; using ll = long long; const int MOD=1000000007; const int MOD2=998244353; const int INF=1<<30; const ll INF2=(ll)1<<60; //入力系 void scan(int& a){scanf("%d",&a);} void scan(long long& a){scanf("%lld",&a);} templatevoid scan(pair& p){scan(p.first);scan(p.second);} template void scan(T& a){cin>>a;} template void scan(vector& vec){for(auto&& it:vec)scan(it);} void in(){} template void in(Head& head, Tail&... tail){scan(head);in(tail...);} //出力系 void print(const int& a){printf("%d",a);} void print(const long long& a){printf("%lld",a);} void print(const double& a){printf("%.15lf",a);} templatevoid print(const pair& p){print(p.first);putchar(' ');print(p.second);} template void print(const T& a){cout< void print(const vector& vec){if(vec.empty())return;print(vec[0]);for(auto it=vec.begin();++it!= vec.end();){putchar(' ');print(*it);}} void out(){putchar('\n');} template void out(const T& t){print(t);putchar('\n');} template void out(const Head& head,const Tail&... tail){print(head);putchar(' ');out(tail...);} //デバッグ系 template void dprint(const T& a){cerr< void dprint(const vector& vec){if(vec.empty())return;cerr< void debug(const T& t){dprint(t);cerr< void debug(const Head& head, const Tail&... tail){dprint(head);cerr<<" ";debug(tail...);} ll intpow(ll a, ll b){ ll ans = 1; while(b){ if(b & 1) ans *= a; a *= a; b /= 2; } return ans; } ll modpow(ll a, ll b, ll p){ ll ans = 1; while(b){ if(b & 1) (ans *= a) %= p; (a *= a) %= p; b /= 2; } return ans; } ll updivide(ll a,ll b){if(a%b==0) return a/b;else return (a/b)+1;} template void chmax(T &a,const T b){if(b>a)a=b;} template void chmin(T &a,const T b){if(b vec(n); vec[0]=1; for(ll i=1;i