#include #include #include #include #include #include #include #include #include #include #include #include #include #include constexpr int MOD = 1000000007; //constexpr int MOD = 998244353; #pragma region Macros using namespace std; #define int long long #define double long double constexpr double PI = 3.14159265358979323846; const int INF = 1e12; const int dx[8] = { 1, 0, -1, 0, 1, -1, -1, 1 }; const int dy[8] = { 0, 1, 0, -1, 1, 1, -1, -1 }; const int days[13] = { 0, 31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31 }; #define rep(i,n) for(int i=0;i=0;i--) #define Rrep(i,n) for(int i=n;i>0;i--) #define LAST(x) x[x.size()-1] #define ALL(x) (x).begin(),(x).end() #define MAX(x) *max_element(ALL(x)) #define MIN(x) *min_element(ALL(x) #define RUD(a,b) ((a+b-1)/b) #define sum1_n(n) ((n)*(n+1)/2) #define SUM1n2(n) (n*(2*n+1)*(n+1))/6 #define SUMkn(k,n) (SUM1n(n)-SUM1n(k-1)) #define PB push_back #define Fi first #define Se second int intpow(int a, int n) { // a^nのint ver int ans = a; if (n == 0) return 1; else { rep(i, n - 1) ans *= a; return ans; } } int factorial(int a) { if (a == 0) return 1; else return a * factorial(a - 1); } int nPr(int n, int r) { int s = n - r + 1; int sum = 1; for (int i = s; i <= n; i++) sum *= i; return sum; } int GCD(int a, int b) { if (a < b) swap(a, b); if (b == 0) return a; if (a % b == 0) return b; return GCD(b, a % b); } int LCM(int a, int b) { return a * b / GCD(a, b); } int divisor_count(int n) { //約数の数 int ans = 0; REP(i, sqrt(n)) { if (n % i == 0) ans += 2; if (n == i * i) ans--; } return ans; } int divisor_sum(int n) { //約数の総和 int ans = 0; REP(i, sqrt(n)) { if (n % i == 0) ans += i + n / i; if (n == i * i) ans -= n / i; } return ans; } int CEIL1(int n) { //1桁目切り上げ return (n + 9) / 10 * 10; } int getdigit(int n) { return log10(n) + 1; } /* int digit(int n, int k) { //nのk桁目 rep(i, k - 1) n /= 10; return n % 10; } */ int digit_sum(int n) { int sum = 0, dig; while (n) { dig = n % 10; sum += dig; n /= 10; } return sum; } int DIVTIME(int n, int k) { //nをkで何回割れるか的な int div = 0; while (n % k == 0) { div++; n /= k; } return div; } #pragma region base /* int n_decimal(int k, int n) { int ans = 0; for (int i = 0; k > 0; i++) { ans += k % n * intpow(10, i); k /= n; } return ans; } */ int binary_2to10(string n) { int ans = 0; rep(i, n.size()) { if (n[i] == '1') ans += intpow(2, n.size() - i - 1); } return ans; } string base_k(int n,int k) { //n(10)をk進数(string)で string ans = ""; while (n) { ans += to_string(n % k); n /= k; } reverse(ALL(ans)); return ans; } #pragma endregion int intabs(int n) { if (n < 0) return -1 * n; else return n; } /* int Kaibun(int n) { int ans = 0; int d = getdigit(n); REP(i, d) ans += digit(n, i) * pow(10, d - i); return ans; } */ inline bool is_uru(int y) { if (y % 400 == 0) return 1; if (y % 100 == 0) return 0; if (y % 4 == 0) return 1; return 0; } void next_date(int& y, int& m, int& d) { int day = days[m]; if (m == 2 && is_uru(y)) day++; d++; if (day < d) { m++; d = 1; } if (m == 13) { y++; m = 1; } } double LOG(int a, int b) { return log(b) / log(a); } double DISTANCE(int x1, int y1, int x2, int y2) { return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2)); } double clock_angle(int h, int m) { h %= 12; double mm = 6.0 * m; double nn = 30.0 * h + 0.5 * m; return std::min(fabs(mm - nn), 360.0 - fabs(nn - mm)); } double heron(double a, double b, double c) { double s = (a + b + c) / 2.0; return sqrt(s * (s - a) * (s - b) * (s - c)); } inline bool BETWEEN(int x, int min, int max) { if (min <= x && x <= max) return true; else return false; } inline bool between(int x, int min, int max) { if (min < x && x < max) return true; else return false; } inline bool is_prime(int x) { if (x == 1) return false; if (x == 2) return true; if (x % 2 == 0) return false; double sqrtx = sqrt(x); for (int i = 3; i <= sqrtx; i += 2) { if (x % i == 0) return false; } return true; } inline bool is_sqrt(int n) { if (sqrt(n) == (int)sqrt(n)) return true; else return false; } template inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; } template inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; } #define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl #pragma endregion typedef vector vint; typedef vector vvint; typedef vector vvvint; typedef vector vstring; typedef vector vbool; typedef vector vvbool; typedef map mapint; typedef pair pint; typedef vector vpint; using Graph = vector; #pragma region MOD template struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v% MOD) { if (val < 0) val += MOD; } constexpr int getmod() const { return MOD; } constexpr Fp operator - () const noexcept { return val ? MOD - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % MOD; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } friend constexpr istream& operator >> (istream& is, Fp& x) noexcept { is >> x.val; x.val %= MOD; if (x.val < 0) x.val += MOD; return is; } friend constexpr ostream& operator << (ostream& os, const Fp& x) noexcept { return os << x.val; } friend constexpr Fp modpow(const Fp& r, long long n) noexcept { if (n == 0) return 1; if (n < 0) return modpow(modinv(r), -n); auto t = modpow(r, n / 2); t = t * t; if (n & 1) t = t * r; return t; } friend constexpr Fp modinv(const Fp& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b, swap(a, b); u -= t * v, swap(u, v); } return Fp(u); } }; using mint = Fp; #pragma endregion #pragma region nCr const int MAXR = 10000000; int fac[MAXR], finv[MAXR], inv[MAXR]; void COMinit() { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < MAXR; i++) { fac[i] = fac[i - 1] * i % MOD; inv[i] = MOD - inv[MOD % i] * (MOD / i) % MOD; finv[i] = finv[i - 1] * inv[i] % MOD; } } int nCr(int n, int k) { if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % MOD) % MOD; } mint nCrm(long long N, long long K) { mint res = 1; for (long long n = 0; n < K; ++n) { res *= (N - n); res /= (n + 1); } return res; } int nCr2(int n, int r) { //MODらない奴 int ans = 1; REP(i, r) { ans *= n--; ans /= i; } return ans; } #pragma endregion vector prime_factorize(int N) { vector res; for(int i=2;i*i<=N;i++){ if (N % i != 0) continue; int ex = 0; while (N % i == 0) { ++ex; N /= i; } res.push_back({ i, ex }); } if (N != 1) res.push_back({ N, 1 }); return res; } double median(vint a) { int N = a.size(); if (N % 2 == 1) return (double)a[N / 2]; else return (double)(a[N / 2 - 1] + a[N / 2]) / 2; } char z(char a, char b) { if (a > b) swap(a, b); if (a == b) return a; if (a == 'R' && b == 'S') return 'R'; if (a == 'P' && b == 'R') return 'P'; if (a == 'P' && b == 'S') return 'S'; } int sum_xor(int x) { if (x % 4 == 1) return 1; if (x % 4 == 3) return 0; return (x + 1) ^ sum_xor(x + 1); } struct UnionFind { //自身が親であれば、その集合に属する頂点数に-1を掛けたもの //そうでなければ親のid vint r; UnionFind(int N) { r = vint(N, -1); } int root(int x) { if (r[x] < 0) return x; return r[x] = root(r[x]); } bool is_same(int x, int y) { return root(x) == root(y); } bool unite(int x, int y) { x = root(x); y = root(y); if (x == y) return false; if (r[x] > r[y]) swap(x, y); r[x] += r[y]; r[y] = x; return true; } int size(int x) { return -r[root(x)]; } }; #pragma region Segment Tree #define len (1<<22) int seg[len * 2]; void add(int ind, int v) { ind += len; seg[ind] += v; while (ind/2!=0) { ind /= 2; seg[ind] = seg[ind * 2]+seg[ind * 2 + 1]; } } int sum(int l, int r) { l += len, r += len; int ans = 0; while (l> x; rep(i, x.size()) { if (x[i] == '?') cout << y[i] << endl; } } //2分探索テンプレ /* bool solve() { } int l= int r= int mid; while(abs(l-r)>1){ mid = l + (r-l)/2; if(solve(mid)) l = mid; else r = mid; } */ //bit全探索テンプレ /* rep(bit,1<> N >> M; Graph G(N + 1); rep(i, M) { int a, b; cin >> a >> b; G[a].push_back(b); G[b].push_back(a); } */ //グラフ型BFSテンプレ /* vector dist(N+1, -1); queue que; dist[1] = 0; que.push(1); while (!que.empty()) { int v = que.front(); que.pop(); for (int nv : G[v]) { if (dist[nv] != -1) continue; dist[nv] = dist[v] + 1; que.push(nv); } } */ //グリッド型BFSテンプレ /* vvint dist(H, vint(W, -1)); dist[sx][sy] = 0; queue que; que.push({sx, sy}); while (!que.empty()) { pint cu = que.front(); que.pop(); rep(i,4){ int nx = cu.first + dx[i]; int ny = cu.second + dy[i]; if (nx < 0 || nx >= H || ny < 0 || ny >= W || S[nx][ny] == '#') continue; if (dist[nx][ny] == -1) { que.push({nx, ny}); dist[nx][ny] = dist[cu.first][cu.second] + 1; } } } 多点スタートなら rep(i,H){ rep(j,W){ if (S[i][j] == '#') { dist[i][j] = 0; que.push({ i, j }); } } } */ //素因数分解する時のやつ /* const auto& res = prime_factorize(N); for (auto p : res) { } */ //グラフデバッグ /* REP(i, N) { cout << "G[" << i << "]="; rep(j, G[i].size) cout << G[i][j] << " "; cout << endl; } */ // fixed << setprecision(15)<< // << setw(2) << setfill('0') /* /*int NumberofDivsors(int N) { vector a = Prime_factorize(N); int ans = 1; for (pint p : a) ans *= p.second() + 1; return ans; } */ //xor /* a^a=0 a^x^x == a a^x == b^x <=> a == b a+b==a^b ⇔ a&b==0 a+b=a^b+2(a&b) 4a^(4a+1)^(4a+2)^(4a+3)=0 */