#pragma region Macros #pragma GCC optimize("O3") #include #define ll long long #define ld long double #define rep2(i,a,b) for(ll i=a;i<=b;++i) #define rep(i,n) for(ll i=0;i=b;i--) #define pii pair #define pll pair #define pq priority_queue #define pb push_back #define eb emplace_back #define vec vector #define vecll vector #define vecpii vector #define vecpll vector #define vec2(a,b) vector(a,vec(b)) #define vec2ll(a,b) vector(a,vecll(b)) #define vec3(a,b,c) vector>(a,vec2(b,c)) #define vec3ll(a,b,c) vector>(a,vec2ll(b,c)) #define fi first #define se second #define all(c) begin(c),end(c) #define ios ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0); #define lb(c,x) distance(c.begin(),lower_bound(all(c),(x))) #define ub(c,x) distance(c.begin(),upper_bound(all(c),(x))) using namespace std; int in() {int x;cin>>x;return x;} ll lin() {ll x;cin>>x;return x;} string stin() {string s;cin>>s;return s;} template inline bool chmax(T& a,T b){if(a inline bool chmin(T& a,T b){if(a>b){a=b;return 1;}return 0;} vec iota(int n){vec a(n);iota(all(a),0);return a;} void print(){putchar(' ');} void print(bool a){cout< void print(const vector&); template void print(const array&); template void print(const pair& p); template void print(const T (&)[size]); template void print(const vector& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout<<" "; print(*i); } cout< void print(const deque& a){ if(a.empty()) return; print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout<<" "; print(*i); } } template void print(const array& a){ print(a[0]); for(auto i = a.begin(); ++i != a.end(); ){ cout<<" "; print(*i); } } template void print(const pair& p){ cout<<'(';print(p.first); cout<<","; print(p.second);cout<<')'; } template void print(const T (&a)[size]){ print(a[0]); for(auto i = a; ++i != end(a); ){ cout<<" "; print(*i); } } template void print(const T& a){ cout << a; } int out(){ putchar('\n'); return 0; } template int out(const T& t){ print(t); putchar('\n'); return 0; } template int out(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); return 0; } ll gcd(ll a, ll b){ while(b){ ll c = b; b = a % b; a = c; } return a; } ll lcm(ll a, ll b){ if(!a || !b) return 0; return a * b / gcd(a, b); } vector factor(ll x){ vector ans; for(ll i = 2; i * i <= x; i++) if(x % i == 0){ ans.push_back({i, 1}); while((x /= i) % i == 0) ans.back().second++; } if(x != 1) ans.push_back({x, 1}); return ans; } vector divisor(int x){ vector ans; for(int i=1;i*i<=x;i++)if(x%i==0){ans.pb(i);if(i*i!=x)ans.pb(x/i);} return ans;} template void UNIQUE(vector &x){sort(all(x));x.erase(unique(all(x)),x.end());} int popcount(ll x){return __builtin_popcountll(x);} mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); int rnd(int n){return uniform_int_distribution(0, n)(rng);} #define _GLIBCXX_DEBU #define endl '\n' #ifdef _MY_DEBUG #undef endl #define debug(x) cout<<#x<<": "< void err(const T& t){ print(t); cout<<" ";} template void err(const Head& head, const Tail&... tail){ print(head); putchar(' '); out(tail...); } #else #define debug(x) template void err(const T&...){} #endif #pragma endregion const ll MOD=1e9+7; const int N=1100000; template class modint { using u64 = ll; public: u64 a; constexpr modint(const u64 x = 0) noexcept : a(((x % Modulus) + Modulus)%Modulus) {} constexpr u64 &value() noexcept { return a; } constexpr const u64 &value() const noexcept { return a; } 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 { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr modint &operator-=(const modint rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr modint &operator*=(const modint rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr modint &operator/=(modint rhs) noexcept { u64 exp = Modulus - 2; while (exp) { if (exp % 2) { *this *= rhs; } rhs *= rhs; exp /= 2; } return *this; } }; #define mint modint mint inv[N],comb[N],prd[N],invprd[N]; void calc_inv(){ inv[1]=1; rep2(i,2,N-1){ inv[i]=inv[MOD%i]*(-MOD/i); } return; } void calc_product(){ prd[0]=prd[1]=1; invprd[0]=invprd[1]=1; rep2(i,2,N-1){ prd[i]=prd[i-1]*i; invprd[i]=inv[i]*invprd[i-1]; } return ; } mint cmb(int a,int b){ if(a ; ostream& operator<<(ostream& os, mint a){ os << a.a ; return os; } signed main(){ ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);cout<