#include #pragma GCC target("avx2") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") using namespace std; using ll=long long; using ld=long double; using ull=unsigned long long; using i128 = __int128_t; #define rep(i,n) for(ll i=0;i=0;i--) #define rep3(i,a,b) for(ll i=a;i<=ll(b);i++) #define rep4(i,a,b) for(ll i=a;i>=ll(b);i--) #define forv(i,V) for(const auto& i:V) #define all(x) x.begin(),x.end() #define fi first #define se second #define SIZE(x) int(x.size()) //constexpr ll mod=998244353; //constexpr ll mod=1000000007; #define pi 3.14159265358979323 #define INF32 2147483647 #define INF64 9223372036854775807 #define faster ios::sync_with_stdio(false);std::cin.tie(nullptr) #define pii pair #define pll pair #define pb push_back #define eb emplace_back #define mp make_pair #define rev reverse #define vi vector #define vll vector #define vpi vector> #define vpll vector> #define vvi vector> #define vvll vector> #define prq priority_queue #define lb lower_bound #define ub upper_bound #define popcnt __builtin_popcountll #define TLE while(true) #define RE assert(false); #define MLE vector>> mle_mle(400,vector>(1000,vector(1000))); const string YESNO[2] = {"NO", "YES"}; const string YesNo[2] = {"No", "Yes"}; const string yesno[2] = {"no", "yes"}; #define rall(n) (n).rbegin(),(n).rend() #define INT(...) int __VA_ARGS__;scan(__VA_ARGS__) #define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__) #define STR(...) string __VA_ARGS__;scan(__VA_ARGS__) #define CHR(...) char __VA_ARGS__;scan(__VA_ARGS__) #define DBL(...) double __VA_ARGS__;scan(__VA_ARGS__) #define LD(...) ld __VA_ARGS__;scan(__VA_ARGS__) template ostream &operator<<(ostream&os,const pair&p){os< istream &operator>>(istream&is,pair&p){is>>p.first>>p.second;return is;} template ostream &operator<<(ostream&os,const vector&v){for(auto it=v.begin();it!=v.end();){os<<*it<<((++it)!=v.end()?" ":"");}return os;} template istream &operator>>(istream&is,vector&v){for(T &in:v){is>>in;}return is;} void scan(){} template void scan(Head&head,Tail&... tail){cin>>head;scan(tail...);} template void print(const T &t){cout< void print(const Head &head, const Tail &... tail){cout< void fin(const T &... a){print(a...);exit(0);} ll max(int a,ll b){return max((ll)a,b);} ll max(ll a,int b){return max((ll)b,a);} ll min(int a,ll b){return min((ll)a,b);} ll min(ll a,int b){return min((ll)b,a);} //a以上b以下の個数 template ll RangeOK(ll a,ll b,vector &v){ return max(ub(all(v),b)-lb(all(v),a),0); } template vector compress(vector &X) { vector vals = X; sort(vals.begin(), vals.end()); vals.erase(unique(vals.begin(), vals.end()), vals.end()); for (int i = 0; i < (int)X.size(); i++) { X[i] = lower_bound(vals.begin(), vals.end(), X[i]) - vals.begin(); } return vals; } //setprecision(20) namespace yakisoba{ struct dsu{ dsu() : _n(0) {} dsu(int n) : _n(n), parent(n, -1), groupsize(n) {} int merge(int a,int b){ if(a<0||a>=_n||b<0||b>=_n) cerr<<"UnionFind Range out:"<parent[y]) swap(x,y); parent[x]+=parent[y]; parent[y]=x; return x; } bool same(int a,int b){ if(a<0||a>=_n||b<0||b>=_n) cerr<<"UnionFind Range out:"<=_n) cerr<<"UnionFind Range out:"<=_n) cerr<<"UnionFind Range out:"<> groups(){ vector group_size(_n),leader_list(_n); for(int i=0;i<_n;i++){ leader_list[i]=leader(i); group_size[leader_list[i]]++; } vector> ans(_n); for(int i=0;i<_n;i++){ ans[i].reserve(group_size[i]); } for(int i=0;i<_n;i++){ ans[leader_list[i]].push_back(i); } ans.erase(remove_if(ans.begin(),ans.end(),[&](const vector& v){return v.empty();}),ans.end()); return ans; } public: int groupsize; private: //代表元はそのグループの要素数を符号を反転させて持つ //それ以外は親を持つ int _n; vector parent; }; } using namespace yakisoba; struct Barrett { using u32=unsigned int; using i64=long long; using u64=unsigned long long; u32 m; u64 im; Barrett():m(),im(){} Barrett(int n):m(n),im(u64(-1)/m+1){} constexpr inline i64 quo(u64 n){ u64 x=u64((__uint128_t(n)*im)>>64); u32 r=n-x*m; return m<=r?x-1:x; } constexpr inline i64 rem(u64 n){ u64 x=u64((__uint128_t(n)*im)>>64); u32 r=n-x*m; return m<=r?r+m:r; } constexpr inline pair quorem(u64 n){ u64 x=u64((__uint128_t(n)*im)>>64); u32 r=n-x*m; if(m<=r)return{x-1,r+m}; return{x,r}; } constexpr inline i64 pow(u64 n,i64 p){ u32 a=rem(n),r=m==1?0:1; while(p){ if(p&1)r=rem(u64(r)*a); a=rem(u64(a)*a); p>>=1; } return r; } }; struct Amint{ int get() const {return x;} inline unsigned int rem(unsigned long long p){return barrett().rem(p);} static inline Barrett &barrett(){ static Barrett b; return b; } static inline int &get_mod(){ static int modp = 0; return modp; } static void set_mod(int md){ assert(0=get_mod())x-=get_mod(); return *this; } Amint &operator-=(const Amint &p){ if((x+=get_mod()-p.x)>=get_mod())x-=get_mod(); return *this; } Amint &operator*=(const Amint &p){ x=rem((unsigned long long)x*p.x); return *this; } Amint &operator/=(const Amint &p){ *this *=p.inv(); return *this; } Amint &operator++(){ if(++x==get_mod()) x=0; return *this; } Amint &operator--(){ if(x--==0) x=get_mod()-1; return *this; } Amint operator-() const{return Amint(-x);} Amint operator+(const Amint &p) const{ return Amint(*this)+=p; } Amint operator-(const Amint &p) const{ return Amint(*this)-=p; } Amint operator*(const Amint &p) const{ return Amint(*this)*= p; } Amint operator/(const Amint &p) const{ return Amint(*this)/= p; } bool operator==(const Amint &p) const {return x==p.x;} bool operator!=(const Amint &p) const {return x!=p.x;} bool operator<(const Amint &p) const {return x(const Amint &p) const {return x>p.x;} bool operator<=(const Amint &p) const {return x<=p.x;} bool operator>=(const Amint &p) const {return x>=p.x;} Amint pow(int64_t n) const{ Amint r(1),m(x); while(n>0){ if (n&1) r*=m; m*=m; n>>=1; } return r; } Amint inv() const{ int a=x,b=get_mod(),u=1,v=0,t; while(b>0){ t=a/b; swap(a-=t*b,b); swap(u-=t*v,v); } return Amint(u); } friend ostream &operator<<(ostream &os,const Amint &p){ return os<>(istream &is,Amint &a){ int64_t t; is>>t; a=Amint(t); return(is); } }; template struct modint{ int get() const{return x;} static constexpr int get_mod(){return modp;} int x; modint():x(0){} modint(int64_t y):x(y>=0?y%modp:(modp-(-y)%modp)%modp){} modint &operator+=(const modint &p){ if((x+=p.x)>=modp)x-=modp; return *this; } modint &operator-=(const modint &p){ if((x+=modp-p.x)>=modp)x-=modp; return *this; } modint &operator*=(const modint &p){ x=(int)(1LL*x*p.x%modp); return *this; } modint &operator/=(const modint &p){ *this*=p.inverse(); return *this; } modint operator-() const{return modint(-x);} modint operator+(const modint &p) const{ return modint(*this)+=p; } modint operator-(const modint &p) const{ return modint(*this)-=p; } modint operator*(const modint &p) const{ return modint(*this)*= p; } modint operator/(const modint &p) const{ return modint(*this)/= p; } modint &operator++(){ if(++x==get_mod()) x=0; return *this; } modint &operator--(){ if(x--==0) x=get_mod()-1; return *this; } bool operator==(const modint &p) const {return x==p.x;} bool operator!=(const modint &p) const {return x!=p.x;} bool operator<(const modint &p) const {return x(const modint &p) const {return x>p.x;} bool operator<=(const modint &p) const {return x<=p.x;} bool operator>=(const modint &p) const {return x>=p.x;} modint pow(int64_t n) const{ modint r(1),m(x); while(n>0){ if (n&1) r*=m; m*=m; n>>=1; } return r; } modint inv()const{ int a=x,b=get_mod(),u=1,v=0,t; while(b>0){ t=a/b; swap(a-=t*b,b); swap(u-=t*v,v); } return modint(u); } friend ostream &operator<<(ostream &os,const modint &p){ return os<>(istream &is,modint &a){ int64_t t; is>>t; a=modint(t); return(is); } }; #define mint Amint //#define MOD Amint::set_mod(1000000007); #define MOD Amint::set_mod(998244353); //#define mint modint //modが不変の場合は上3つを利用 //modが10^9+7と998244353の時は, MOD; を最初に実行する //modが可変の場合は1番下を利用 mint<998244353>のように宣言 long long pow(long long n,long long k){ long long ans=1; while(k){ if(k&1) ans*=n; n*=n; k>>=1; } return ans; } //modをとらない場合の累乗 modをとる場合はa.pow(1000)のようにmodintを使う mint comb_naive(mint n,mint k){ if(k<0||n fac(k_max); vector inv_fac(k_max); void set_comb(){ MOD; fac[0]=1; for(mint i=1;i=1;--i){ inv_fac[i.get()]=inv_fac[i.get()+1]*(i+1); } } mint comb(mint n,mint k){ if(k<0||n v(n); scan(v); mint ans=0; rep(i,n){ ans+=v[i]*(mint(2).pow(n-i-1)-1); ans-=v[i]*(mint(2).pow(i)-1); } fin(ans); }