#include #include #include #include #include #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { int ceil_pow2(int n) { int x = 0; while ((1U << x) < (unsigned int)(n)) x++; return x; } constexpr int bsf_constexpr(unsigned int n) { int x = 0; while (!(n & (1 << x))) x++; return x; } int bsf(unsigned int n) { #ifdef _MSC_VER unsigned long index; _BitScanForward(&index, n); return index; #else return __builtin_ctz(n); #endif } } // namespace internal } // namespace atcoder #include #include #include #ifdef _MSC_VER #include #endif #include #ifdef _MSC_VER #include #endif namespace atcoder { namespace internal { constexpr long long safe_mod(long long x, long long m) { x %= m; if (x < 0) x += m; return x; } struct barrett { unsigned int _m; unsigned long long im; explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {} unsigned int umod() const { return _m; } unsigned int mul(unsigned int a, unsigned int b) const { unsigned long long z = a; z *= b; #ifdef _MSC_VER unsigned long long x; _umul128(z, im, &x); #else unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64); #endif unsigned int v = (unsigned int)(z - x * _m); if (_m <= v) v += _m; return v; } }; constexpr long long pow_mod_constexpr(long long x, long long n, int m) { if (m == 1) return 0; unsigned int _m = (unsigned int)(m); unsigned long long r = 1; unsigned long long y = safe_mod(x, m); while (n) { if (n & 1) r = (r * y) % _m; y = (y * y) % _m; n >>= 1; } return r; } constexpr bool is_prime_constexpr(int n) { if (n <= 1) return false; if (n == 2 || n == 7 || n == 61) return true; if (n % 2 == 0) return false; long long d = n - 1; while (d % 2 == 0) d /= 2; constexpr long long bases[3] = {2, 7, 61}; for (long long a : bases) { long long t = d; long long y = pow_mod_constexpr(a, t, n); while (t != n - 1 && y != 1 && y != n - 1) { y = y * y % n; t <<= 1; } if (y != n - 1 && t % 2 == 0) { return false; } } return true; } template constexpr bool is_prime = is_prime_constexpr(n); constexpr std::pair inv_gcd(long long a, long long b) { a = safe_mod(a, b); if (a == 0) return {b, 0}; long long s = b, t = a; long long m0 = 0, m1 = 1; while (t) { long long u = s / t; s -= t * u; m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b auto tmp = s; s = t; t = tmp; tmp = m0; m0 = m1; m1 = tmp; } if (m0 < 0) m0 += b / s; return {s, m0}; } constexpr int primitive_root_constexpr(int m) { if (m == 2) return 1; if (m == 167772161) return 3; if (m == 469762049) return 3; if (m == 754974721) return 11; if (m == 998244353) return 3; int divs[20] = {}; divs[0] = 2; int cnt = 1; int x = (m - 1) / 2; while (x % 2 == 0) x /= 2; for (int i = 3; (long long)(i)*i <= x; i += 2) { if (x % i == 0) { divs[cnt++] = i; while (x % i == 0) { x /= i; } } } if (x > 1) { divs[cnt++] = x; } for (int g = 2;; g++) { bool ok = true; for (int i = 0; i < cnt; i++) { if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) { ok = false; break; } } if (ok) return g; } } template constexpr int primitive_root = primitive_root_constexpr(m); unsigned long long floor_sum_unsigned(unsigned long long n, unsigned long long m, unsigned long long a, unsigned long long b) { unsigned long long ans = 0; while (true) { if (a >= m) { ans += n * (n - 1) / 2 * (a / m); a %= m; } if (b >= m) { ans += n * (b / m); b %= m; } unsigned long long y_max = a * n + b; if (y_max < m) break; n = (unsigned long long)(y_max / m); b = (unsigned long long)(y_max % m); std::swap(m, a); } return ans; } } // namespace internal } // namespace atcoder #include #include #include namespace atcoder { namespace internal { #ifndef _MSC_VER template using is_signed_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using is_unsigned_int128 = typename std::conditional::value || std::is_same::value, std::true_type, std::false_type>::type; template using make_unsigned_int128 = typename std::conditional::value, __uint128_t, unsigned __int128>; template using is_integral = typename std::conditional::value || is_signed_int128::value || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using is_signed_int = typename std::conditional<(is_integral::value && std::is_signed::value) || is_signed_int128::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional<(is_integral::value && std::is_unsigned::value) || is_unsigned_int128::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional< is_signed_int128::value, make_unsigned_int128, typename std::conditional::value, std::make_unsigned, std::common_type>::type>::type; #else template using is_integral = typename std::is_integral; template using is_signed_int = typename std::conditional::value && std::is_signed::value, std::true_type, std::false_type>::type; template using is_unsigned_int = typename std::conditional::value && std::is_unsigned::value, std::true_type, std::false_type>::type; template using to_unsigned = typename std::conditional::value, std::make_unsigned, std::common_type>::type; #endif template using is_signed_int_t = std::enable_if_t::value>; template using is_unsigned_int_t = std::enable_if_t::value>; template using to_unsigned_t = typename to_unsigned::type; } // namespace internal } // namespace atcoder namespace atcoder { namespace internal { struct modint_base {}; struct static_modint_base : modint_base {}; template using is_modint = std::is_base_of; template using is_modint_t = std::enable_if_t::value>; } // namespace internal template * = nullptr> struct static_modint : internal::static_modint_base { using mint = static_modint; public: static constexpr int mod() { return m; } static mint raw(int v) { mint x; x._v = v; return x; } static_modint() : _v(0) {} template * = nullptr> static_modint(T v) { long long x = (long long)(v % (long long)(umod())); if (x < 0) x += umod(); _v = (unsigned int)(x); } template * = nullptr> static_modint(T v) { _v = (unsigned int)(v % umod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v -= rhs._v; if (_v >= umod()) _v += umod(); return *this; } mint& operator*=(const mint& rhs) { unsigned long long z = _v; z *= rhs._v; _v = (unsigned int)(z % umod()); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { if (prime) { assert(_v); return pow(umod() - 2); } else { auto eg = internal::inv_gcd(_v, m); assert(eg.first == 1); return eg.second; } } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static constexpr unsigned int umod() { return m; } static constexpr bool prime = internal::is_prime; }; template struct dynamic_modint : internal::modint_base { using mint = dynamic_modint; public: static int mod() { return (int)(bt.umod()); } static void set_mod(int m) { assert(1 <= m); bt = internal::barrett(m); } static mint raw(int v) { mint x; x._v = v; return x; } dynamic_modint() : _v(0) {} template * = nullptr> dynamic_modint(T v) { long long x = (long long)(v % (long long)(mod())); if (x < 0) x += mod(); _v = (unsigned int)(x); } template * = nullptr> dynamic_modint(T v) { _v = (unsigned int)(v % mod()); } unsigned int val() const { return _v; } mint& operator++() { _v++; if (_v == umod()) _v = 0; return *this; } mint& operator--() { if (_v == 0) _v = umod(); _v--; return *this; } mint operator++(int) { mint result = *this; ++*this; return result; } mint operator--(int) { mint result = *this; --*this; return result; } mint& operator+=(const mint& rhs) { _v += rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator-=(const mint& rhs) { _v += mod() - rhs._v; if (_v >= umod()) _v -= umod(); return *this; } mint& operator*=(const mint& rhs) { _v = bt.mul(_v, rhs._v); return *this; } mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); } mint operator+() const { return *this; } mint operator-() const { return mint() - *this; } mint pow(long long n) const { assert(0 <= n); mint x = *this, r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } mint inv() const { auto eg = internal::inv_gcd(_v, mod()); assert(eg.first == 1); return eg.second; } friend mint operator+(const mint& lhs, const mint& rhs) { return mint(lhs) += rhs; } friend mint operator-(const mint& lhs, const mint& rhs) { return mint(lhs) -= rhs; } friend mint operator*(const mint& lhs, const mint& rhs) { return mint(lhs) *= rhs; } friend mint operator/(const mint& lhs, const mint& rhs) { return mint(lhs) /= rhs; } friend bool operator==(const mint& lhs, const mint& rhs) { return lhs._v == rhs._v; } friend bool operator!=(const mint& lhs, const mint& rhs) { return lhs._v != rhs._v; } private: unsigned int _v; static internal::barrett bt; static unsigned int umod() { return bt.umod(); } }; template internal::barrett dynamic_modint::bt(998244353); using modint998244353 = static_modint<998244353>; using modint1000000007 = static_modint<1000000007>; using modint = dynamic_modint<-1>; namespace internal { template using is_static_modint = std::is_base_of; template using is_static_modint_t = std::enable_if_t::value>; template struct is_dynamic_modint : public std::false_type {}; template struct is_dynamic_modint> : public std::true_type {}; template using is_dynamic_modint_t = std::enable_if_t::value>; } // namespace internal } // namespace atcoder namespace atcoder { namespace internal { template , internal::is_static_modint_t* = nullptr> struct fft_info { static constexpr int rank2 = bsf_constexpr(mint::mod() - 1); std::array root; // root[i]^(2^i) == 1 std::array iroot; // root[i] * iroot[i] == 1 std::array rate2; std::array irate2; std::array rate3; std::array irate3; fft_info() { root[rank2] = mint(g).pow((mint::mod() - 1) >> rank2); iroot[rank2] = root[rank2].inv(); for (int i = rank2 - 1; i >= 0; i--) { root[i] = root[i + 1] * root[i + 1]; iroot[i] = iroot[i + 1] * iroot[i + 1]; } { mint prod = 1, iprod = 1; for (int i = 0; i <= rank2 - 2; i++) { rate2[i] = root[i + 2] * prod; irate2[i] = iroot[i + 2] * iprod; prod *= iroot[i + 2]; iprod *= root[i + 2]; } } { mint prod = 1, iprod = 1; for (int i = 0; i <= rank2 - 3; i++) { rate3[i] = root[i + 3] * prod; irate3[i] = iroot[i + 3] * iprod; prod *= iroot[i + 3]; iprod *= root[i + 3]; } } } }; template * = nullptr> void butterfly(std::vector& a) { int n = int(a.size()); int h = internal::ceil_pow2(n); static const fft_info info; int len = 0; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed while (len < h) { if (h - len == 1) { int p = 1 << (h - len - 1); mint rot = 1; for (int s = 0; s < (1 << len); s++) { int offset = s << (h - len); for (int i = 0; i < p; i++) { auto l = a[i + offset]; auto r = a[i + offset + p] * rot; a[i + offset] = l + r; a[i + offset + p] = l - r; } if (s + 1 != (1 << len)) rot *= info.rate2[bsf(~(unsigned int)(s))]; } len++; } else { int p = 1 << (h - len - 2); mint rot = 1, imag = info.root[2]; for (int s = 0; s < (1 << len); s++) { mint rot2 = rot * rot; mint rot3 = rot2 * rot; int offset = s << (h - len); for (int i = 0; i < p; i++) { auto mod2 = 1ULL * mint::mod() * mint::mod(); auto a0 = 1ULL * a[i + offset].val(); auto a1 = 1ULL * a[i + offset + p].val() * rot.val(); auto a2 = 1ULL * a[i + offset + 2 * p].val() * rot2.val(); auto a3 = 1ULL * a[i + offset + 3 * p].val() * rot3.val(); auto a1na3imag = 1ULL * mint(a1 + mod2 - a3).val() * imag.val(); auto na2 = mod2 - a2; a[i + offset] = a0 + a2 + a1 + a3; a[i + offset + 1 * p] = a0 + a2 + (2 * mod2 - (a1 + a3)); a[i + offset + 2 * p] = a0 + na2 + a1na3imag; a[i + offset + 3 * p] = a0 + na2 + (mod2 - a1na3imag); } if (s + 1 != (1 << len)) rot *= info.rate3[bsf(~(unsigned int)(s))]; } len += 2; } } } template * = nullptr> void butterfly_inv(std::vector& a) { int n = int(a.size()); int h = internal::ceil_pow2(n); static const fft_info info; int len = h; // a[i, i+(n>>len), i+2*(n>>len), ..] is transformed while (len) { if (len == 1) { int p = 1 << (h - len); mint irot = 1; for (int s = 0; s < (1 << (len - 1)); s++) { int offset = s << (h - len + 1); for (int i = 0; i < p; i++) { auto l = a[i + offset]; auto r = a[i + offset + p]; a[i + offset] = l + r; a[i + offset + p] = (unsigned long long)(mint::mod() + l.val() - r.val()) * irot.val(); ; } if (s + 1 != (1 << (len - 1))) irot *= info.irate2[bsf(~(unsigned int)(s))]; } len--; } else { int p = 1 << (h - len); mint irot = 1, iimag = info.iroot[2]; for (int s = 0; s < (1 << (len - 2)); s++) { mint irot2 = irot * irot; mint irot3 = irot2 * irot; int offset = s << (h - len + 2); for (int i = 0; i < p; i++) { auto a0 = 1ULL * a[i + offset + 0 * p].val(); auto a1 = 1ULL * a[i + offset + 1 * p].val(); auto a2 = 1ULL * a[i + offset + 2 * p].val(); auto a3 = 1ULL * a[i + offset + 3 * p].val(); auto a2na3iimag = 1ULL * mint((mint::mod() + a2 - a3) * iimag.val()).val(); a[i + offset] = a0 + a1 + a2 + a3; a[i + offset + 1 * p] = (a0 + (mint::mod() - a1) + a2na3iimag) * irot.val(); a[i + offset + 2 * p] = (a0 + a1 + (mint::mod() - a2) + (mint::mod() - a3)) * irot2.val(); a[i + offset + 3 * p] = (a0 + (mint::mod() - a1) + (mint::mod() - a2na3iimag)) * irot3.val(); } if (s + 1 != (1 << (len - 2))) irot *= info.irate3[bsf(~(unsigned int)(s))]; } len -= 2; } } } template * = nullptr> std::vector convolution_naive(const std::vector& a, const std::vector& b) { int n = int(a.size()), m = int(b.size()); std::vector ans(n + m - 1); if (n < m) { for (int j = 0; j < m; j++) { for (int i = 0; i < n; i++) { ans[i + j] += a[i] * b[j]; } } } else { for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) { ans[i + j] += a[i] * b[j]; } } } return ans; } template * = nullptr> std::vector convolution_fft(std::vector a, std::vector b) { int n = int(a.size()), m = int(b.size()); int z = 1 << internal::ceil_pow2(n + m - 1); a.resize(z); internal::butterfly(a); b.resize(z); internal::butterfly(b); for (int i = 0; i < z; i++) { a[i] *= b[i]; } internal::butterfly_inv(a); a.resize(n + m - 1); mint iz = mint(z).inv(); for (int i = 0; i < n + m - 1; i++) a[i] *= iz; return a; } } // namespace internal template * = nullptr> std::vector convolution(std::vector&& a, std::vector&& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; if (std::min(n, m) <= 60) return convolution_naive(a, b); return internal::convolution_fft(a, b); } template * = nullptr> std::vector convolution(const std::vector& a, const std::vector& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; if (std::min(n, m) <= 60) return convolution_naive(a, b); return internal::convolution_fft(a, b); } template ::value>* = nullptr> std::vector convolution(const std::vector& a, const std::vector& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; using mint = static_modint; std::vector a2(n), b2(m); for (int i = 0; i < n; i++) { a2[i] = mint(a[i]); } for (int i = 0; i < m; i++) { b2[i] = mint(b[i]); } auto c2 = convolution(move(a2), move(b2)); std::vector c(n + m - 1); for (int i = 0; i < n + m - 1; i++) { c[i] = c2[i].val(); } return c; } std::vector convolution_ll(const std::vector& a, const std::vector& b) { int n = int(a.size()), m = int(b.size()); if (!n || !m) return {}; static constexpr unsigned long long MOD1 = 754974721; // 2^24 static constexpr unsigned long long MOD2 = 167772161; // 2^25 static constexpr unsigned long long MOD3 = 469762049; // 2^26 static constexpr unsigned long long M2M3 = MOD2 * MOD3; static constexpr unsigned long long M1M3 = MOD1 * MOD3; static constexpr unsigned long long M1M2 = MOD1 * MOD2; static constexpr unsigned long long M1M2M3 = MOD1 * MOD2 * MOD3; static constexpr unsigned long long i1 = internal::inv_gcd(MOD2 * MOD3, MOD1).second; static constexpr unsigned long long i2 = internal::inv_gcd(MOD1 * MOD3, MOD2).second; static constexpr unsigned long long i3 = internal::inv_gcd(MOD1 * MOD2, MOD3).second; auto c1 = convolution(a, b); auto c2 = convolution(a, b); auto c3 = convolution(a, b); std::vector c(n + m - 1); for (int i = 0; i < n + m - 1; i++) { unsigned long long x = 0; x += (c1[i] * i1) % MOD1 * M2M3; x += (c2[i] * i2) % MOD2 * M1M3; x += (c3[i] * i3) % MOD3 * M1M2; long long diff = c1[i] - internal::safe_mod((long long)(x), (long long)(MOD1)); if (diff < 0) diff += MOD1; static constexpr unsigned long long offset[5] = { 0, 0, M1M2M3, 2 * M1M2M3, 3 * M1M2M3}; x -= offset[diff % 5]; c[i] = x; } return c; } } // namespace atcoder #include #include #include namespace atcoder { struct dsu { public: dsu() : _n(0) {} explicit dsu(int n) : _n(n), parent_or_size(n, -1) {} int merge(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); int x = leader(a), y = leader(b); if (x == y) return x; if (-parent_or_size[x] < -parent_or_size[y]) std::swap(x, y); parent_or_size[x] += parent_or_size[y]; parent_or_size[y] = x; return x; } bool same(int a, int b) { assert(0 <= a && a < _n); assert(0 <= b && b < _n); return leader(a) == leader(b); } int leader(int a) { assert(0 <= a && a < _n); if (parent_or_size[a] < 0) return a; return parent_or_size[a] = leader(parent_or_size[a]); } int size(int a) { assert(0 <= a && a < _n); return -parent_or_size[leader(a)]; } std::vector> groups() { std::vector leader_buf(_n), group_size(_n); for (int i = 0; i < _n; i++) { leader_buf[i] = leader(i); group_size[leader_buf[i]]++; } std::vector> result(_n); for (int i = 0; i < _n; i++) { result[i].reserve(group_size[i]); } for (int i = 0; i < _n; i++) { result[leader_buf[i]].push_back(i); } result.erase( std::remove_if(result.begin(), result.end(), [&](const std::vector& v) { return v.empty(); }), result.end()); return result; } private: int _n; std::vector parent_or_size; }; } // namespace atcoder #include #include namespace atcoder { template struct fenwick_tree { using U = internal::to_unsigned_t; public: fenwick_tree() : _n(0) {} explicit fenwick_tree(int n) : _n(n), data(n) {} void add(int p, T x) { assert(0 <= p && p < _n); p++; while (p <= _n) { data[p - 1] += U(x); p += p & -p; } } T sum(int l, int r) { assert(0 <= l && l <= r && r <= _n); return sum(r) - sum(l); } private: int _n; std::vector data; U sum(int r) { U s = 0; while (r > 0) { s += data[r - 1]; r -= r & -r; } return s; } }; } // namespace atcoder #include #include #include #include namespace atcoder { template struct lazy_segtree { public: lazy_segtree() : lazy_segtree(0) {} explicit lazy_segtree(int n) : lazy_segtree(std::vector(n, e())) {} explicit lazy_segtree(const std::vector& v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector(2 * size, e()); lz = std::vector(size, id()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); return d[p]; } S prod(int l, int r) { assert(0 <= l && l <= r && r <= _n); if (l == r) return e(); l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } S sml = e(), smr = e(); while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() { return d[1]; } void apply(int p, F f) { assert(0 <= p && p < _n); p += size; for (int i = log; i >= 1; i--) push(p >> i); d[p] = mapping(f, d[p]); for (int i = 1; i <= log; i++) update(p >> i); } void apply(int l, int r, F f) { assert(0 <= l && l <= r && r <= _n); if (l == r) return; l += size; r += size; for (int i = log; i >= 1; i--) { if (((l >> i) << i) != l) push(l >> i); if (((r >> i) << i) != r) push((r - 1) >> i); } { int l2 = l, r2 = r; while (l < r) { if (l & 1) all_apply(l++, f); if (r & 1) all_apply(--r, f); l >>= 1; r >>= 1; } l = l2; r = r2; } for (int i = 1; i <= log; i++) { if (((l >> i) << i) != l) update(l >> i); if (((r >> i) << i) != r) update((r - 1) >> i); } } template int max_right(int l) { return max_right(l, [](S x) { return g(x); }); } template int max_right(int l, G g) { assert(0 <= l && l <= _n); assert(g(e())); if (l == _n) return _n; l += size; for (int i = log; i >= 1; i--) push(l >> i); S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!g(op(sm, d[l]))) { while (l < size) { push(l); l = (2 * l); if (g(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template int min_left(int r) { return min_left(r, [](S x) { return g(x); }); } template int min_left(int r, G g) { assert(0 <= r && r <= _n); assert(g(e())); if (r == 0) return 0; r += size; for (int i = log; i >= 1; i--) push((r - 1) >> i); S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!g(op(d[r], sm))) { while (r < size) { push(r); r = (2 * r + 1); if (g(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; std::vector d; std::vector lz; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } void all_apply(int k, F f) { d[k] = mapping(f, d[k]); if (k < size) lz[k] = composition(f, lz[k]); } void push(int k) { all_apply(2 * k, lz[k]); all_apply(2 * k + 1, lz[k]); lz[k] = id(); } }; } // namespace atcoder #include #include #include #include namespace atcoder { long long pow_mod(long long x, long long n, int m) { assert(0 <= n && 1 <= m); if (m == 1) return 0; internal::barrett bt((unsigned int)(m)); unsigned int r = 1, y = (unsigned int)(internal::safe_mod(x, m)); while (n) { if (n & 1) r = bt.mul(r, y); y = bt.mul(y, y); n >>= 1; } return r; } long long inv_mod(long long x, long long m) { assert(1 <= m); auto z = internal::inv_gcd(x, m); assert(z.first == 1); return z.second; } std::pair crt(const std::vector& r, const std::vector& m) { assert(r.size() == m.size()); int n = int(r.size()); long long r0 = 0, m0 = 1; for (int i = 0; i < n; i++) { assert(1 <= m[i]); long long r1 = internal::safe_mod(r[i], m[i]), m1 = m[i]; if (m0 < m1) { std::swap(r0, r1); std::swap(m0, m1); } if (m0 % m1 == 0) { if (r0 % m1 != r1) return {0, 0}; continue; } long long g, im; std::tie(g, im) = internal::inv_gcd(m0, m1); long long u1 = (m1 / g); if ((r1 - r0) % g) return {0, 0}; long long x = (r1 - r0) / g % u1 * im % u1; r0 += x * m0; m0 *= u1; // -> lcm(m0, m1) if (r0 < 0) r0 += m0; } return {r0, m0}; } long long floor_sum(long long n, long long m, long long a, long long b) { assert(0 <= n && n < (1LL << 32)); assert(1 <= m && m < (1LL << 32)); unsigned long long ans = 0; if (a < 0) { unsigned long long a2 = internal::safe_mod(a, m); ans -= 1ULL * n * (n - 1) / 2 * ((a2 - a) / m); a = a2; } if (b < 0) { unsigned long long b2 = internal::safe_mod(b, m); ans -= 1ULL * n * ((b2 - b) / m); b = b2; } return ans + internal::floor_sum_unsigned(n, m, a, b); } } // namespace atcoder #include #include #include #include #include #include namespace atcoder { namespace internal { template struct simple_queue { std::vector payload; int pos = 0; void reserve(int n) { payload.reserve(n); } int size() const { return int(payload.size()) - pos; } bool empty() const { return pos == int(payload.size()); } void push(const T& t) { payload.push_back(t); } T& front() { return payload[pos]; } void clear() { payload.clear(); pos = 0; } void pop() { pos++; } }; } // namespace internal } // namespace atcoder namespace atcoder { template struct mf_graph { public: mf_graph() : _n(0) {} explicit mf_graph(int n) : _n(n), g(n) {} int add_edge(int from, int to, Cap cap) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); int m = int(pos.size()); pos.push_back({from, int(g[from].size())}); int from_id = int(g[from].size()); int to_id = int(g[to].size()); if (from == to) to_id++; g[from].push_back(_edge{to, to_id, cap}); g[to].push_back(_edge{from, from_id, 0}); return m; } struct edge { int from, to; Cap cap, flow; }; edge get_edge(int i) { int m = int(pos.size()); assert(0 <= i && i < m); auto _e = g[pos[i].first][pos[i].second]; auto _re = g[_e.to][_e.rev]; return edge{pos[i].first, _e.to, _e.cap + _re.cap, _re.cap}; } std::vector edges() { int m = int(pos.size()); std::vector result; for (int i = 0; i < m; i++) { result.push_back(get_edge(i)); } return result; } void change_edge(int i, Cap new_cap, Cap new_flow) { int m = int(pos.size()); assert(0 <= i && i < m); assert(0 <= new_flow && new_flow <= new_cap); auto& _e = g[pos[i].first][pos[i].second]; auto& _re = g[_e.to][_e.rev]; _e.cap = new_cap - new_flow; _re.cap = new_flow; } Cap flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } Cap flow(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); std::vector level(_n), iter(_n); internal::simple_queue que; auto bfs = [&]() { std::fill(level.begin(), level.end(), -1); level[s] = 0; que.clear(); que.push(s); while (!que.empty()) { int v = que.front(); que.pop(); for (auto e : g[v]) { if (e.cap == 0 || level[e.to] >= 0) continue; level[e.to] = level[v] + 1; if (e.to == t) return; que.push(e.to); } } }; auto dfs = [&](auto self, int v, Cap up) { if (v == s) return up; Cap res = 0; int level_v = level[v]; for (int& i = iter[v]; i < int(g[v].size()); i++) { _edge& e = g[v][i]; if (level_v <= level[e.to] || g[e.to][e.rev].cap == 0) continue; Cap d = self(self, e.to, std::min(up - res, g[e.to][e.rev].cap)); if (d <= 0) continue; g[v][i].cap += d; g[e.to][e.rev].cap -= d; res += d; if (res == up) return res; } level[v] = _n; return res; }; Cap flow = 0; while (flow < flow_limit) { bfs(); if (level[t] == -1) break; std::fill(iter.begin(), iter.end(), 0); Cap f = dfs(dfs, t, flow_limit - flow); if (!f) break; flow += f; } return flow; } std::vector min_cut(int s) { std::vector visited(_n); internal::simple_queue que; que.push(s); while (!que.empty()) { int p = que.front(); que.pop(); visited[p] = true; for (auto e : g[p]) { if (e.cap && !visited[e.to]) { visited[e.to] = true; que.push(e.to); } } } return visited; } private: int _n; struct _edge { int to, rev; Cap cap; }; std::vector> pos; std::vector> g; }; } // namespace atcoder #include #include #include #include #include #include #include #include namespace atcoder { namespace internal { template struct csr { std::vector start; std::vector elist; explicit csr(int n, const std::vector>& edges) : start(n + 1), elist(edges.size()) { for (auto e : edges) { start[e.first + 1]++; } for (int i = 1; i <= n; i++) { start[i] += start[i - 1]; } auto counter = start; for (auto e : edges) { elist[counter[e.first]++] = e.second; } } }; } // namespace internal } // namespace atcoder namespace atcoder { template struct mcf_graph { public: mcf_graph() {} explicit mcf_graph(int n) : _n(n) {} int add_edge(int from, int to, Cap cap, Cost cost) { assert(0 <= from && from < _n); assert(0 <= to && to < _n); assert(0 <= cap); assert(0 <= cost); int m = int(_edges.size()); _edges.push_back({from, to, cap, 0, cost}); return m; } struct edge { int from, to; Cap cap, flow; Cost cost; }; edge get_edge(int i) { int m = int(_edges.size()); assert(0 <= i && i < m); return _edges[i]; } std::vector edges() { return _edges; } std::pair flow(int s, int t) { return flow(s, t, std::numeric_limits::max()); } std::pair flow(int s, int t, Cap flow_limit) { return slope(s, t, flow_limit).back(); } std::vector> slope(int s, int t) { return slope(s, t, std::numeric_limits::max()); } std::vector> slope(int s, int t, Cap flow_limit) { assert(0 <= s && s < _n); assert(0 <= t && t < _n); assert(s != t); int m = int(_edges.size()); std::vector edge_idx(m); auto g = [&]() { std::vector degree(_n), redge_idx(m); std::vector> elist; elist.reserve(2 * m); for (int i = 0; i < m; i++) { auto e = _edges[i]; edge_idx[i] = degree[e.from]++; redge_idx[i] = degree[e.to]++; elist.push_back({e.from, {e.to, -1, e.cap - e.flow, e.cost}}); elist.push_back({e.to, {e.from, -1, e.flow, -e.cost}}); } auto _g = internal::csr<_edge>(_n, elist); for (int i = 0; i < m; i++) { auto e = _edges[i]; edge_idx[i] += _g.start[e.from]; redge_idx[i] += _g.start[e.to]; _g.elist[edge_idx[i]].rev = redge_idx[i]; _g.elist[redge_idx[i]].rev = edge_idx[i]; } return _g; }(); auto result = slope(g, s, t, flow_limit); for (int i = 0; i < m; i++) { auto e = g.elist[edge_idx[i]]; _edges[i].flow = _edges[i].cap - e.cap; } return result; } private: int _n; std::vector _edges; struct _edge { int to, rev; Cap cap; Cost cost; }; std::vector> slope(internal::csr<_edge>& g, int s, int t, Cap flow_limit) { std::vector> dual_dist(_n); std::vector prev_e(_n); std::vector vis(_n); struct Q { Cost key; int to; bool operator<(Q r) const { return key > r.key; } }; std::vector que_min; std::vector que; auto dual_ref = [&]() { for (int i = 0; i < _n; i++) { dual_dist[i].second = std::numeric_limits::max(); } std::fill(vis.begin(), vis.end(), false); que_min.clear(); que.clear(); size_t heap_r = 0; dual_dist[s].second = 0; que_min.push_back(s); while (!que_min.empty() || !que.empty()) { int v; if (!que_min.empty()) { v = que_min.back(); que_min.pop_back(); } else { while (heap_r < que.size()) { heap_r++; std::push_heap(que.begin(), que.begin() + heap_r); } v = que.front().to; std::pop_heap(que.begin(), que.end()); que.pop_back(); heap_r--; } if (vis[v]) continue; vis[v] = true; if (v == t) break; Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second; for (int i = g.start[v]; i < g.start[v + 1]; i++) { auto e = g.elist[i]; if (!e.cap) continue; Cost cost = e.cost - dual_dist[e.to].first + dual_v; if (dual_dist[e.to].second - dist_v > cost) { Cost dist_to = dist_v + cost; dual_dist[e.to].second = dist_to; prev_e[e.to] = e.rev; if (dist_to == dist_v) { que_min.push_back(e.to); } else { que.push_back(Q{dist_to, e.to}); } } } } if (!vis[t]) { return false; } for (int v = 0; v < _n; v++) { if (!vis[v]) continue; dual_dist[v].first -= dual_dist[t].second - dual_dist[v].second; } return true; }; Cap flow = 0; Cost cost = 0, prev_cost_per_flow = -1; std::vector> result = {{Cap(0), Cost(0)}}; while (flow < flow_limit) { if (!dual_ref()) break; Cap c = flow_limit - flow; for (int v = t; v != s; v = g.elist[prev_e[v]].to) { c = std::min(c, g.elist[g.elist[prev_e[v]].rev].cap); } for (int v = t; v != s; v = g.elist[prev_e[v]].to) { auto& e = g.elist[prev_e[v]]; e.cap += c; g.elist[e.rev].cap -= c; } Cost d = -dual_dist[s].first; flow += c; cost += c * d; if (prev_cost_per_flow == d) { result.pop_back(); } result.push_back({flow, cost}); prev_cost_per_flow = d; } return result; } }; } // namespace atcoder #include #include #include #include #include #include namespace atcoder { namespace internal { struct scc_graph { public: explicit scc_graph(int n) : _n(n) {} int num_vertices() { return _n; } void add_edge(int from, int to) { edges.push_back({from, {to}}); } std::pair> scc_ids() { auto g = csr(_n, edges); int now_ord = 0, group_num = 0; std::vector visited, low(_n), ord(_n, -1), ids(_n); visited.reserve(_n); auto dfs = [&](auto self, int v) -> void { low[v] = ord[v] = now_ord++; visited.push_back(v); for (int i = g.start[v]; i < g.start[v + 1]; i++) { auto to = g.elist[i].to; if (ord[to] == -1) { self(self, to); low[v] = std::min(low[v], low[to]); } else { low[v] = std::min(low[v], ord[to]); } } if (low[v] == ord[v]) { while (true) { int u = visited.back(); visited.pop_back(); ord[u] = _n; ids[u] = group_num; if (u == v) break; } group_num++; } }; for (int i = 0; i < _n; i++) { if (ord[i] == -1) dfs(dfs, i); } for (auto& x : ids) { x = group_num - 1 - x; } return {group_num, ids}; } std::vector> scc() { auto ids = scc_ids(); int group_num = ids.first; std::vector counts(group_num); for (auto x : ids.second) counts[x]++; std::vector> groups(ids.first); for (int i = 0; i < group_num; i++) { groups[i].reserve(counts[i]); } for (int i = 0; i < _n; i++) { groups[ids.second[i]].push_back(i); } return groups; } private: int _n; struct edge { int to; }; std::vector> edges; }; } // namespace internal } // namespace atcoder namespace atcoder { struct scc_graph { public: scc_graph() : internal(0) {} explicit scc_graph(int n) : internal(n) {} void add_edge(int from, int to) { int n = internal.num_vertices(); assert(0 <= from && from < n); assert(0 <= to && to < n); internal.add_edge(from, to); } std::vector> scc() { return internal.scc(); } private: internal::scc_graph internal; }; } // namespace atcoder #include #include #include namespace atcoder { template struct segtree { public: segtree() : segtree(0) {} explicit segtree(int n) : segtree(std::vector(n, e())) {} explicit segtree(const std::vector& v) : _n(int(v.size())) { log = internal::ceil_pow2(_n); size = 1 << log; d = std::vector(2 * size, e()); for (int i = 0; i < _n; i++) d[size + i] = v[i]; for (int i = size - 1; i >= 1; i--) { update(i); } } void set(int p, S x) { assert(0 <= p && p < _n); p += size; d[p] = x; for (int i = 1; i <= log; i++) update(p >> i); } S get(int p) const { assert(0 <= p && p < _n); return d[p + size]; } S prod(int l, int r) const { assert(0 <= l && l <= r && r <= _n); S sml = e(), smr = e(); l += size; r += size; while (l < r) { if (l & 1) sml = op(sml, d[l++]); if (r & 1) smr = op(d[--r], smr); l >>= 1; r >>= 1; } return op(sml, smr); } S all_prod() const { return d[1]; } template int max_right(int l) const { return max_right(l, [](S x) { return f(x); }); } template int max_right(int l, F f) const { assert(0 <= l && l <= _n); assert(f(e())); if (l == _n) return _n; l += size; S sm = e(); do { while (l % 2 == 0) l >>= 1; if (!f(op(sm, d[l]))) { while (l < size) { l = (2 * l); if (f(op(sm, d[l]))) { sm = op(sm, d[l]); l++; } } return l - size; } sm = op(sm, d[l]); l++; } while ((l & -l) != l); return _n; } template int min_left(int r) const { return min_left(r, [](S x) { return f(x); }); } template int min_left(int r, F f) const { assert(0 <= r && r <= _n); assert(f(e())); if (r == 0) return 0; r += size; S sm = e(); do { r--; while (r > 1 && (r % 2)) r >>= 1; if (!f(op(d[r], sm))) { while (r < size) { r = (2 * r + 1); if (f(op(d[r], sm))) { sm = op(d[r], sm); r--; } } return r + 1 - size; } sm = op(d[r], sm); } while ((r & -r) != r); return 0; } private: int _n, size, log; std::vector d; void update(int k) { d[k] = op(d[2 * k], d[2 * k + 1]); } }; } // namespace atcoder ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////// #include using namespace std; using namespace atcoder; typedef long long ll; //typedef int ll; void mod_print(ll k){ // const ll i_7=998244353; const ll i_7 =(ll)(1E9+7); auto mod=[&](ll a){ ll c=a%i_7; if(c>=0)return c; return c+i_7; }; ll P=50000; for(ll y=1;y<=P;y++){ ll x=mod(y*k); if(abs(x)<=P||x+P>=i_7){ if(x+P>=i_7){ x-=i_7; } cerr< #include namespace multi = boost::multiprecision; typedef multi::cpp_int LL; typedef multi::number> DD;// 仮数部が1024ビットの浮動小数点数型(TLEしたら小さくする) //*/ typedef long double dd; typedef pair l_l; typedef pair d_d; ll inf=(ll)1E18; #define rep(i,l,r) for(ll i=l;i<=r;i++) #define rrep(i,r,l) for(ll i=r;i>=l;i--) #define pb push_back ll max(ll a,ll b){if(ab)return b;else return a;} dd EPS=1E-12; #define fi first #define se second #define SORT(v) sort(v.begin(),v.end()) #define ERASE(v) sort(v.begin(),v.end()); v.erase(unique(v.begin(),v.end()),v.end()) #define POSL(v,x) (lower_bound(v.begin(),v.end(),x)-v.begin()) #define POSU(v,x) (upper_bound(v.begin(),v.end(),x)-v.begin()) template inline bool chmax(T &a, S b) { if(a < b) { a = (T)b; return true; } return false; } template inline bool chmin(T &a, S b) { if(a > b) { a = (T)b; return true; } return false; } #define all(c) c.begin(),c.end() //using mint = modint998244353; using mint = modint1000000007; //using mint=modint; //using mint=static_modint<100>; //using mint=dd; //using mint=ll; typedef vector vl; typedef vector vvl; typedef vectorvvvl; typedef vectorvvvvl; typedef vectorvi; typedef vectorvvi; typedef vectorvvvi; typedef vectorvvvvi; typedef pairi_i; typedef vectorvi_i; typedef vectorvl_l; typedef vectorvvl_l; typedef vectorvs; typedef vectorvvs; typedef vector
vd; typedef vector vvd; typedef vector vvvd; typedef vectorvd_d; dd PI=acos((dd)-1); #define fastio ios::sync_with_stdio(false); cin.tie(0); cout.tie(0); cout< using pq = priority_queue; template using pqg = priority_queue, greater>; // g++ -std=gnu++17 -Wall -Wextra -O2 -DONLINE_JUDGE main.cpp && ./a.out //#define endl "\n" //インタラクティブで消す!!!!!!!!!!!!!!!!!!!!! #define popcount __builtin_popcountll #define SHUFFLE(v) shuffle(all(v),default_random_engine(chrono::system_clock::now().time_since_epoch().count())) ////////////////////////////////////////////////////////////////////////////// template void DEBUG_PRINT(S x){ cerr< void DEBUG_PRINT(pairx){ cerr<<"("< void DEBUG_PRINT(vector x){ for(auto y:x)cerr< void DEBUG_PRINT(vector>x){ for(auto y:x)cerr<<"("< void DEBUG_PRINT(vector> x){ cerr< struct Edge { int src, to; Cost cost; Edge(int s, int t, Cost c = 1) : src(s), to(t), cost(c) {} operator int() const { return to; } //これのおかげで、辺をint型として扱うこともできる }; template struct Graph : vector>> { Graph(int n) : vector>>(n) {} void add_edge(int s, int t, Cost c = 1) { (*this)[s].emplace_back(s, t, c); } }; template struct Rerooting : Graph { vector dp, memo; Rerooting(int n) : Graph::Graph(n) {} vector run() { memo.resize((*this).size(), e()); dp.resize((*this).size()); if((int)((*this).size()) == 1){ dp[0] = leaf(0); return dp; } ll root=0; while(1){ if((int)((*this)[root].size()) == 1){ break; } root++; } cerr<<"root is "< &d : (*this)[c]) { if (d == p) continue; //dをint型として扱ってる dfs1(d, c); upd = true; memo[c] = merge(memo[c], apply(memo[d], d, c, d.cost));//d.costの部分は、dをEdge型として扱ってる } if (!upd) memo[c] = leaf(c); } void dfs2(int c, int p, const Data &val) { vector ds{val}; //親から降ってきた値がds[0]に入ってる for (Edge &d : (*this)[c]) { if (d == p) continue; ds.push_back(apply(memo[d], d, c, d.cost)); } int n = ds.size(), idx = 1; //親から降ってきた値がds[0]に入ってるので、idxは1からスタート vector head(n + 1, e()), tail(n + 1, e()); for (int i = 0; i++ < n;) head[i] = merge(head[i - 1], ds[i - 1]); for (int i = n; i-- > 0;) tail[i] = merge(tail[i + 1], ds[i]); dp[c] = head[n]; for (Edge &d : (*this)[c]) { if (d == p) continue; Data sub = merge(head[idx], tail[idx + 1]); dfs2(d, c, apply(sub, c, d, d.cost)); idx++; } } }; //ここより上は変更しなくていい /////////////////////////////////////////////////////////////////////////////////////////// const vl emp(30); using Data = vl; //dpテーブルの値の型 using Cost = ll; //辺のコストの型 Data merge(Data a, Data b) { rep(i,0,29)a[i] += b[i]; return a; } Data e() {return emp; } //単位元 Data leaf(int pos) { return emp; } //頂点が葉である時、その頂点のdpの値 Data apply(Data dpc, int c, int p, Cost w) { //(親がp,子がc,コストがw)となる辺があって、子のdpの値がdpcのとき、親に返す値 //親のdpの値が変更されるとは限らないので、dp[p] = merge(dp[p], apply( hoge )) というイメージ rep(i,0,29){ if(!((w>>i)&1))dpc[i]=0; else dpc[i]++; } return dpc; } //木は 0-indexed!!!! //Rerootingg(n); //メモ:Dataに部分木のサイズを保存する時、部分木の根はサイズに含まないようにしたほうがよい。 //参考 https://atcoder.jp/contests/abc160/submissions/26429038 // https://atcoder.jp/contests/abc220/submissions/26429495 ///////////////////////////////////////////////////////////////////////////////////////////// signed main(){fastio ll n;cin>>n; Rerootingg(n); rep(i,1,n-1){ ll a,b,c;cin>>a>>b>>c; a--;b--; g.add_edge(a,b,c); g.add_edge(b,a,c); } auto ret = g.run(); //DEB(ret); mint ans=0; for(auto x:ret){ rep(i,0,29){ ans += (mint)x[i] * (1ll<