結果
| 問題 | No.235 めぐるはめぐる (5) |
| ユーザー |
 kuhaku
|
| 提出日時 | 2025-02-24 21:19:27 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,692 ms / 10,000 ms |
| コード長 | 42,220 bytes |
| コンパイル時間 | 5,202 ms |
| コンパイル使用メモリ | 324,048 KB |
| 実行使用メモリ | 28,132 KB |
| 最終ジャッジ日時 | 2025-02-24 21:19:42 |
| 合計ジャッジ時間 | 13,323 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 3 |
ソースコード
// competitive-verifier: PROBLEM
#include <iostream>
#include <vector>
/**
* @brief 重み付きグラフ
*
* @tparam T 辺の重みの型
*/
template <class T>
struct Graph {
private:
struct _edge {
constexpr _edge() : _from(), _to(), _weight() {}
constexpr _edge(int from, int to, T weight) : _from(from), _to(to), _weight(weight) {}
constexpr bool operator<(const _edge &rhs) const { return weight() < rhs.weight(); }
constexpr bool operator>(const _edge &rhs) const { return rhs < *this; }
constexpr int from() const { return _from; }
constexpr int to() const { return _to; }
constexpr T weight() const { return _weight; }
private:
int _from, _to;
T _weight;
};
public:
using edge_type = typename Graph<T>::_edge;
Graph() : _size(), edges() {}
Graph(int v) : _size(v), edges(v) {}
const auto &operator[](int i) const { return edges[i]; }
auto &operator[](int i) { return edges[i]; }
const auto begin() const { return edges.begin(); }
auto begin() { return edges.begin(); }
const auto end() const { return edges.end(); }
auto end() { return edges.end(); }
constexpr int size() const { return _size; }
void add_edge(const edge_type &e) { edges[e.from()].emplace_back(e); }
void add_edge(int from, int to, T weight = T(1)) { edges[from].emplace_back(from, to, weight); }
void add_edges(int from, int to, T weight = T(1)) {
edges[from].emplace_back(from, to, weight);
edges[to].emplace_back(to, from, weight);
}
void input_edge(int m, int base = 1) {
for (int i = 0; i < m; ++i) {
int from, to;
T weight;
std::cin >> from >> to >> weight;
add_edge(from - base, to - base, weight);
}
}
void input_edges(int m, int base = 1) {
for (int i = 0; i < m; ++i) {
int from, to;
T weight;
std::cin >> from >> to >> weight;
add_edges(from - base, to - base, weight);
}
}
private:
int _size;
std::vector<std::vector<edge_type>> edges;
};
template <>
struct Graph<void> {
private:
struct _edge {
constexpr _edge() : _from(), _to() {}
constexpr _edge(int from, int to) : _from(from), _to(to) {}
constexpr int from() const { return _from; }
constexpr int to() const { return _to; }
constexpr int weight() const { return 1; }
constexpr bool operator<(const _edge &rhs) const { return weight() < rhs.weight(); }
constexpr bool operator>(const _edge &rhs) const { return rhs < *this; }
private:
int _from, _to;
};
public:
using edge_type = typename Graph<void>::_edge;
Graph() : _size(), edges() {}
Graph(int v) : _size(v), edges(v) {}
const auto &operator[](int i) const { return edges[i]; }
auto &operator[](int i) { return edges[i]; }
const auto begin() const { return edges.begin(); }
auto begin() { return edges.begin(); }
const auto end() const { return edges.end(); }
auto end() { return edges.end(); }
constexpr int size() const { return _size; }
void add_edge(const edge_type &e) { edges[e.from()].emplace_back(e); }
void add_edge(int from, int to) { edges[from].emplace_back(from, to); }
void add_edges(int from, int to) {
edges[from].emplace_back(from, to);
edges[to].emplace_back(to, from);
}
void input_edge(int m, int base = 1) {
for (int i = 0; i < m; ++i) {
int from, to;
std::cin >> from >> to;
add_edge(from - base, to - base);
}
}
void input_edges(int m, int base = 1) {
for (int i = 0; i < m; ++i) {
int from, to;
std::cin >> from >> to;
add_edges(from - base, to - base);
}
}
private:
int _size;
std::vector<std::vector<edge_type>> edges;
};
#include <cstdint>
#include <type_traits>
#include <utility>
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr std::int64_t safe_mod(std::int64_t x, std::int64_t m) {
x %= m;
if (x < 0) x += m;
return x;
}
// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
unsigned int _m;
std::uint64_t im;
// @param m `1 <= m`
explicit barrett(unsigned int m) : _m(m), im((std::uint64_t)(-1) / m + 1) {}
// @return m
unsigned int umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
unsigned int mul(unsigned int a, unsigned int b) const {
std::uint64_t z = a;
z *= b;
std::uint64_t x = (std::uint64_t)(((__uint128_t)(z)*im) >> 64);
std::uint64_t y = x * _m;
return (unsigned int)(z - y + (z < y ? _m : 0));
}
};
struct montgomery {
std::uint64_t _m;
std::uint64_t im;
std::uint64_t r2;
// @param m `1 <= m`
explicit constexpr montgomery(std::uint64_t m) : _m(m), im(m), r2(-__uint128_t(m) % m) {
for (int i = 0; i < 5; ++i) im = im * (2 - _m * im);
im = -im;
}
// @return m
constexpr std::uint64_t umod() const { return _m; }
// @param a `0 <= a < m`
// @param b `0 <= b < m`
// @return `a * b % m`
constexpr std::uint64_t mul(std::uint64_t a, std::uint64_t b) const { return mr(mr(a, b), r2); }
constexpr std::uint64_t exp(std::uint64_t a, std::uint64_t b) const {
std::uint64_t res = 1, p = mr(a, r2);
while (b) {
if (b & 1) res = mr(res, p);
p = mr(p, p);
b >>= 1;
}
return res;
}
constexpr bool same_pow(std::uint64_t x, int s, std::uint64_t n) const {
x = mr(x, r2), n = mr(n, r2);
for (int r = 0; r < s; r++) {
if (x == n) return true;
x = mr(x, x);
}
return false;
}
private:
constexpr std::uint64_t mr(std::uint64_t x) const {
return ((__uint128_t)(x * im) * _m + x) >> 64;
}
constexpr std::uint64_t mr(std::uint64_t a, std::uint64_t b) const {
__uint128_t t = (__uint128_t)a * b;
std::uint64_t inc = std::uint64_t(t) != 0;
std::uint64_t x = t >> 64, y = ((__uint128_t)(a * b * im) * _m) >> 64;
unsigned long long z = 0;
bool f = __builtin_uaddll_overflow(x, y, &z);
z += inc;
return f ? z - _m : z;
}
};
constexpr bool is_SPRP32(std::uint32_t n, std::uint32_t a) {
std::uint32_t d = n - 1, s = 0;
while ((d & 1) == 0) ++s, d >>= 1;
std::uint64_t cur = 1, pw = d;
while (pw) {
if (pw & 1) cur = (cur * a) % n;
a = (std::uint64_t)a * a % n;
pw >>= 1;
}
if (cur == 1) return true;
for (std::uint32_t r = 0; r < s; r++) {
if (cur == n - 1) return true;
cur = cur * cur % n;
}
return false;
}
// given 2 <= n,a < 2^64, a prime, check whether n is a-SPRP
constexpr bool is_SPRP64(const montgomery &m, std::uint64_t a) {
auto n = m.umod();
if (n == a) return true;
if (n % a == 0) return false;
std::uint64_t d = n - 1;
int s = 0;
while ((d & 1) == 0) ++s, d >>= 1;
std::uint64_t cur = m.exp(a, d);
if (cur == 1) return true;
return m.same_pow(cur, s, n - 1);
}
constexpr bool is_prime_constexpr(std::uint64_t x) {
if (x == 2 || x == 3 || x == 5 || x == 7) return true;
if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
if (x < 121) return (x > 1);
montgomery m(x);
constexpr std::uint64_t bases[] = {2, 325, 9375, 28178, 450775, 9780504, 1795265022};
for (auto a : bases) {
if (!is_SPRP64(m, a)) return false;
}
return true;
}
constexpr bool is_prime_constexpr(std::int64_t x) {
if (x < 0) return false;
return is_prime_constexpr(std::uint64_t(x));
}
constexpr bool is_prime_constexpr(std::uint32_t x) {
if (x == 2 || x == 3 || x == 5 || x == 7) return true;
if (x % 2 == 0 || x % 3 == 0 || x % 5 == 0 || x % 7 == 0) return false;
if (x < 121) return (x > 1);
std::uint64_t h = x;
h = ((h >> 16) ^ h) * 0x45d9f3b;
h = ((h >> 16) ^ h) * 0x45d9f3b;
h = ((h >> 16) ^ h) & 255;
constexpr uint16_t bases[] = {
15591, 2018, 166, 7429, 8064, 16045, 10503, 4399, 1949, 1295, 2776, 3620, 560,
3128, 5212, 2657, 2300, 2021, 4652, 1471, 9336, 4018, 2398, 20462, 10277, 8028,
2213, 6219, 620, 3763, 4852, 5012, 3185, 1333, 6227, 5298, 1074, 2391, 5113,
7061, 803, 1269, 3875, 422, 751, 580, 4729, 10239, 746, 2951, 556, 2206,
3778, 481, 1522, 3476, 481, 2487, 3266, 5633, 488, 3373, 6441, 3344, 17,
15105, 1490, 4154, 2036, 1882, 1813, 467, 3307, 14042, 6371, 658, 1005, 903,
737, 1887, 7447, 1888, 2848, 1784, 7559, 3400, 951, 13969, 4304, 177, 41,
19875, 3110, 13221, 8726, 571, 7043, 6943, 1199, 352, 6435, 165, 1169, 3315,
978, 233, 3003, 2562, 2994, 10587, 10030, 2377, 1902, 5354, 4447, 1555, 263,
27027, 2283, 305, 669, 1912, 601, 6186, 429, 1930, 14873, 1784, 1661, 524,
3577, 236, 2360, 6146, 2850, 55637, 1753, 4178, 8466, 222, 2579, 2743, 2031,
2226, 2276, 374, 2132, 813, 23788, 1610, 4422, 5159, 1725, 3597, 3366, 14336,
579, 165, 1375, 10018, 12616, 9816, 1371, 536, 1867, 10864, 857, 2206, 5788,
434, 8085, 17618, 727, 3639, 1595, 4944, 2129, 2029, 8195, 8344, 6232, 9183,
8126, 1870, 3296, 7455, 8947, 25017, 541, 19115, 368, 566, 5674, 411, 522,
1027, 8215, 2050, 6544, 10049, 614, 774, 2333, 3007, 35201, 4706, 1152, 1785,
1028, 1540, 3743, 493, 4474, 2521, 26845, 8354, 864, 18915, 5465, 2447, 42,
4511, 1660, 166, 1249, 6259, 2553, 304, 272, 7286, 73, 6554, 899, 2816,
5197, 13330, 7054, 2818, 3199, 811, 922, 350, 7514, 4452, 3449, 2663, 4708,
418, 1621, 1171, 3471, 88, 11345, 412, 1559, 194};
return is_SPRP32(x, bases[h]);
}
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr std::int64_t pow_mod_constexpr(std::int64_t x, std::int64_t n, int m) {
if (m == 1) return 0;
unsigned int _m = (unsigned int)(m);
std::uint64_t r = 1;
std::uint64_t y = safe_mod(x, m);
while (n) {
if (n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
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;
std::int64_t d = n - 1;
while (d % 2 == 0) d /= 2;
constexpr std::int64_t bases[3] = {2, 7, 61};
for (std::int64_t a : bases) {
std::int64_t t = d;
std::int64_t 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 <int n>
constexpr bool is_prime = is_prime_constexpr(n);
// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<std::int64_t, std::int64_t> inv_gcd(std::int64_t a, std::int64_t b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
std::int64_t s = b, t = a;
std::int64_t m0 = 0, m1 = 1;
while (t) {
std::int64_t u = s / t;
s -= t * u;
m0 -= m1 * u;
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if (m0 < 0) m0 += b / s;
return {s, m0};
}
// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
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; (std::int64_t)(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 <int m>
constexpr int primitive_root = primitive_root_constexpr(m);
} // namespace internal
#include <cassert>
#include <numeric>
namespace internal {
template <class T>
using is_signed_int128 = typename std::conditional<std::is_same<T, __int128_t>::value ||
std::is_same<T, __int128>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int128 = typename std::conditional<std::is_same<T, __uint128_t>::value ||
std::is_same<T, unsigned __int128>::value,
std::true_type, std::false_type>::type;
template <class T>
using make_unsigned_int128 =
typename std::conditional<std::is_same<T, __int128_t>::value, __uint128_t, unsigned __int128>;
template <class T>
using is_integral =
typename std::conditional<std::is_integral<T>::value || is_signed_int128<T>::value ||
is_unsigned_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_signed_int =
typename std::conditional<(is_integral<T>::value && std::is_signed<T>::value) ||
is_signed_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using is_unsigned_int =
typename std::conditional<(is_integral<T>::value && std::is_unsigned<T>::value) ||
is_unsigned_int128<T>::value,
std::true_type, std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<
is_signed_int128<T>::value, make_unsigned_int128<T>,
typename std::conditional<std::is_signed<T>::value, std::make_unsigned<T>,
std::common_type<T>>::type>::type;
template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;
template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;
template <class T>
using to_unsigned_t = typename to_unsigned<T>::type;
} // namespace internal
namespace internal {
struct modint_base {};
struct static_modint_base : modint_base {};
template <class T>
using is_modint = std::is_base_of<modint_base, T>;
template <class T>
using is_modint_t = std::enable_if_t<is_modint<T>::value>;
} // namespace internal
template <int m, std::enable_if_t<(1 <= m)> * = nullptr>
struct static_modint : internal::static_modint_base {
using mint = static_modint;
public:
static constexpr int mod() { return m; }
static constexpr mint raw(int v) {
mint x;
x._v = v;
return x;
}
constexpr static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T> * = nullptr>
constexpr static_modint(T v) : _v(0) {
std::int64_t x = (std::int64_t)(v % (std::int64_t)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = nullptr>
constexpr static_modint(T v) : _v(0) {
_v = (unsigned int)(v % umod());
}
constexpr unsigned int val() const { return _v; }
constexpr mint &operator++() {
_v++;
if (_v == umod()) _v = 0;
return *this;
}
constexpr mint &operator--() {
if (_v == 0) _v = umod();
_v--;
return *this;
}
constexpr mint operator++(int) {
mint result = *this;
++*this;
return result;
}
constexpr mint operator--(int) {
mint result = *this;
--*this;
return result;
}
constexpr mint &operator+=(const mint &rhs) {
_v += rhs._v;
if (_v >= umod()) _v -= umod();
return *this;
}
constexpr mint &operator-=(const mint &rhs) {
_v -= rhs._v;
if (_v >= umod()) _v += umod();
return *this;
}
constexpr mint &operator*=(const mint &rhs) {
std::uint64_t z = _v;
z *= rhs._v;
_v = (unsigned int)(z % umod());
return *this;
}
constexpr mint &operator/=(const mint &rhs) { return *this = *this * rhs.inv(); }
constexpr mint operator+() const { return *this; }
constexpr mint operator-() const { return mint() - *this; }
constexpr mint pow(std::int64_t n) const {
assert(0 <= n);
mint x = *this, r = 1;
while (n) {
if (n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr 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 constexpr mint operator+(const mint &lhs, const mint &rhs) { return mint(lhs) += rhs; }
friend constexpr mint operator-(const mint &lhs, const mint &rhs) { return mint(lhs) -= rhs; }
friend constexpr mint operator*(const mint &lhs, const mint &rhs) { return mint(lhs) *= rhs; }
friend constexpr mint operator/(const mint &lhs, const mint &rhs) { return mint(lhs) /= rhs; }
friend constexpr bool operator==(const mint &lhs, const mint &rhs) { return lhs._v == rhs._v; }
friend constexpr bool operator!=(const mint &lhs, const mint &rhs) { return lhs._v != rhs._v; }
friend std::istream &operator>>(std::istream &is, mint &rhs) {
std::int64_t t;
is >> t;
rhs = mint(t);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const mint &rhs) {
return os << rhs._v;
}
private:
unsigned int _v;
static constexpr unsigned int umod() { return m; }
static constexpr bool prime = internal::is_prime<m>;
};
template <int id>
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 <class T, internal::is_signed_int_t<T> * = nullptr>
dynamic_modint(T v) {
std::int64_t x = (std::int64_t)(v % (std::int64_t)(mod()));
if (x < 0) x += mod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T> * = 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(std::int64_t 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; }
friend std::istream &operator>>(std::istream &is, mint &rhs) {
std::int64_t t;
is >> t;
rhs = mint(t);
return is;
}
friend constexpr std::ostream &operator<<(std::ostream &os, const mint &rhs) {
return os << rhs._v;
}
private:
unsigned int _v;
static internal::barrett bt;
static unsigned int umod() { return bt.umod(); }
};
template <int id>
internal::barrett dynamic_modint<id>::bt(998244353);
using modint998 = static_modint<998244353>;
using modint107 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
namespace internal {
template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;
template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;
template <class>
struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};
template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;
} // namespace internal
namespace internal {
// @return same with std::bit::bit_ceil
unsigned int bit_ceil(unsigned int n) {
unsigned int x = 1;
while (x < (unsigned int)(n)) x *= 2;
return x;
}
// @param n `1 <= n`
// @return same with std::bit::countl_zero
int countl_zero(unsigned int n) { return __builtin_clz(n); }
// @param n `1 <= n`
// @return same with std::bit::countr_zero
int countr_zero(unsigned int n) { return __builtin_ctz(n); }
// @param n `1 <= n`
// @return same with std::bit::countr_zero
constexpr int countr_zero_constexpr(unsigned int n) {
int x = 0;
while (!(n & (1 << x))) x++;
return x;
}
} // namespace internal
#include <algorithm>
#include <limits>
template <class T>
struct Add {
using value_type = T;
static constexpr T id() { return T(); }
static constexpr T op(const T &lhs, const T &rhs) { return lhs + rhs; }
template <class U>
static constexpr U f(T lhs, U rhs) {
return lhs + rhs;
}
};
template <class T>
struct Mul {
using value_type = T;
static constexpr T id() { return T(1); }
static constexpr T op(const T &lhs, const T &rhs) { return lhs * rhs; }
template <class U>
static constexpr U f(T lhs, U rhs) {
return lhs * rhs;
}
};
template <class T>
struct And {
using value_type = T;
static constexpr T id() { return std::numeric_limits<T>::max(); }
static constexpr T op(const T &lhs, const T &rhs) { return lhs & rhs; }
template <class U>
static constexpr U f(T lhs, U rhs) {
return lhs & rhs;
}
};
template <class T>
struct Or {
using value_type = T;
static constexpr T id() { return T(); }
static constexpr T op(const T &lhs, const T &rhs) { return lhs | rhs; }
template <class U>
static constexpr U f(T lhs, U rhs) {
return lhs | rhs;
}
};
template <class T>
struct Xor {
using value_type = T;
static constexpr T id() { return T(); }
static constexpr T op(const T &lhs, const T &rhs) { return lhs ^ rhs; }
template <class U>
static constexpr U f(T lhs, U rhs) {
return lhs ^ rhs;
}
};
template <class T>
struct Min {
using value_type = T;
static constexpr T id() { return std::numeric_limits<T>::max(); }
static constexpr T op(const T &lhs, const T &rhs) { return std::min(lhs, rhs); }
template <class U>
static constexpr U f(T lhs, U rhs) {
return std::min((U)lhs, rhs);
}
};
template <class T>
struct Max {
using value_type = T;
static constexpr T id() { return std::numeric_limits<T>::lowest(); }
static constexpr T op(const T &lhs, const T &rhs) { return std::max(lhs, rhs); }
template <class U>
static constexpr U f(T lhs, U rhs) {
return std::max((U)lhs, rhs);
}
};
template <class T>
struct Gcd {
using value_type = T;
static constexpr T id() { return std::numeric_limits<T>::max(); }
static constexpr T op(const T &lhs, const T &rhs) {
return lhs == Gcd::id() ? rhs : (rhs == Gcd::id() ? lhs : std::gcd(lhs, rhs));
}
};
template <class T>
struct Lcm {
using value_type = T;
static constexpr T id() { return std::numeric_limits<T>::max(); }
static constexpr T op(const T &lhs, const T &rhs) {
return lhs == Lcm::id() ? rhs : (rhs == Lcm::id() ? lhs : std::lcm(lhs, rhs));
}
};
template <class T>
struct Update {
using value_type = T;
static constexpr T id() { return std::numeric_limits<T>::max(); }
static constexpr T op(const T &lhs, const T &rhs) { return lhs == Update::id() ? rhs : lhs; }
template <class U>
static constexpr U f(T lhs, U rhs) {
return lhs == Update::id() ? rhs : lhs;
}
};
template <class T>
struct Affine {
using P = std::pair<T, T>;
using value_type = P;
static constexpr P id() { return P(1, 0); }
static constexpr P op(P lhs, P rhs) {
return {lhs.first * rhs.first, lhs.first * rhs.second + lhs.second};
}
};
template <class M>
struct Rev {
using T = typename M::value_type;
using value_type = T;
static constexpr T id() { return M::id(); }
static constexpr T op(T lhs, T rhs) { return M::op(rhs, lhs); }
};
/**
* @brief 遅延評価セグメント木
* @see https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp
*
* @tparam S モノイド
* @tparam F モノイド
*/
template <class S, class F>
struct lazy_segment_tree {
private:
using T = typename S::value_type;
using U = typename F::value_type;
public:
lazy_segment_tree() : lazy_segment_tree(0) {}
explicit lazy_segment_tree(int n, T e = S::id()) : lazy_segment_tree(std::vector<T>(n, e)) {}
explicit lazy_segment_tree(const std::vector<T> &v) : _n(int(v.size())) {
_size = internal::bit_ceil(_n);
_log = internal::countr_zero(_size);
data = std::vector<T>(2 * _size, S::id());
lazy = std::vector<U>(_size, F::id());
for (int i = 0; i < _n; i++) data[_size + i] = v[i];
for (int i = _size - 1; i >= 1; --i) update(i);
}
void set(int p, T x) {
assert(0 <= p && p < _n);
p += _size;
for (int i = _log; i >= 1; --i) push(p >> i);
data[p] = x;
for (int i = 1; i <= _log; ++i) update(p >> i);
}
T at(int p) { return get(p); }
T get(int p) {
assert(0 <= p && p < _n);
p += _size;
for (int i = _log; i >= 1; --i) push(p >> i);
return data[p];
}
void apply(int p, U f) {
assert(0 <= p && p < _n);
p += _size;
for (int i = _log; i >= 1; --i) push(p >> i);
data[p] = F::f(f, data[p]);
for (int i = 1; i <= _log; ++i) update(p >> i);
}
void apply(int l, int r, U 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);
}
}
T prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return S::id();
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);
}
T sml = S::id(), smr = S::id();
while (l < r) {
if (l & 1) sml = S::op(sml, data[l++]);
if (r & 1) smr = S::op(data[--r], smr);
l >>= 1, r >>= 1;
}
return S::op(sml, smr);
}
T all_prod() const { return data[1]; }
int max_right(int l, T val) {
auto f = [&val](T v) { return !(val < v); };
return max_right(l, f);
}
template <class G>
int max_right(int l, G g) {
assert(0 <= l && l <= _n);
assert(g(S::id()));
if (l == _n) return _n;
l += _size;
for (int i = _log; i >= 1; i--) push(l >> i);
T sm = S::id();
do {
while (l % 2 == 0) l >>= 1;
if (!g(S::op(sm, data[l]))) {
while (l < _size) {
push(l);
l = (2 * l);
if (g(S::op(sm, data[l]))) {
sm = S::op(sm, data[l]);
l++;
}
}
return l - _size;
}
sm = S::op(sm, data[l]);
l++;
} while ((l & -l) != l);
return _n;
}
int min_left(int l, T val) {
auto f = [&val](T v) { return !(val < v); };
return min_left(l, f);
}
template <class G>
int min_left(int r, G g) {
assert(0 <= r && r <= _n);
assert(g(S::id()));
if (r == 0) return 0;
r += _size;
for (int i = _log; i >= 1; i--) push((r - 1) >> i);
S sm = S::id();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!g(S::op(data[r], sm))) {
while (r < _size) {
push(r);
r = (2 * r + 1);
if (g(S::op(data[r], sm))) {
sm = S::op(data[r], sm);
r--;
}
}
return r + 1 - _size;
}
sm = S::op(data[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, _size, _log;
std::vector<T> data;
std::vector<U> lazy;
void update(int k) { data[k] = S::op(data[2 * k], data[2 * k + 1]); }
void all_apply(int k, U f) {
data[k] = F::f(f, data[k]);
if (k < _size) lazy[k] = F::op(f, lazy[k]);
}
void push(int k) {
all_apply(2 * k, lazy[k]);
all_apply(2 * k + 1, lazy[k]);
lazy[k] = F::id();
}
};
#ifdef ATCODER
#pragma GCC target("sse4.2,avx512f,avx512dq,avx512ifma,avx512cd,avx512bw,avx512vl,bmi2")
#endif
#pragma GCC optimize("Ofast,fast-math,unroll-all-loops")
#include <bits/stdc++.h>
#ifndef ATCODER
#pragma GCC target("sse4.2,avx2,bmi2")
#endif
template <class T, class U>
constexpr bool chmax(T &a, const U &b) {
return a < (T)b ? a = (T)b, true : false;
}
template <class T, class U>
constexpr bool chmin(T &a, const U &b) {
return (T)b < a ? a = (T)b, true : false;
}
constexpr std::int64_t INF = 1000000000000000003;
constexpr int Inf = 1000000003;
constexpr double EPS = 1e-7;
constexpr double PI = 3.14159265358979323846;
#define FOR(i, m, n) for (int i = (m); i < int(n); ++i)
#define FORR(i, m, n) for (int i = (m)-1; i >= int(n); --i)
#define FORL(i, m, n) for (int64_t i = (m); i < int64_t(n); ++i)
#define rep(i, n) FOR (i, 0, n)
#define repn(i, n) FOR (i, 1, n + 1)
#define repr(i, n) FORR (i, n, 0)
#define repnr(i, n) FORR (i, n + 1, 1)
#define all(s) (s).begin(), (s).end()
struct Sonic {
Sonic() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(20);
}
constexpr void operator()() const {}
} sonic;
using namespace std;
using ll = std::int64_t;
using ld = long double;
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
return is >> p.first >> p.second;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
for (T &i : v) is >> i;
return is;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
return os << '(' << p.first << ',' << p.second << ')';
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
for (auto it = v.begin(); it != v.end(); ++it) os << (it == v.begin() ? "" : " ") << *it;
return os;
}
template <class Head, class... Tail>
void co(Head &&head, Tail &&...tail) {
if constexpr (sizeof...(tail) == 0) std::cout << head << '\n';
else std::cout << head << ' ', co(std::forward<Tail>(tail)...);
}
template <class Head, class... Tail>
void ce(Head &&head, Tail &&...tail) {
if constexpr (sizeof...(tail) == 0) std::cerr << head << '\n';
else std::cerr << head << ' ', ce(std::forward<Tail>(tail)...);
}
void Yes(bool is_correct = true) { std::cout << (is_correct ? "Yes\n" : "No\n"); }
void No(bool is_not_correct = true) { Yes(!is_not_correct); }
void YES(bool is_correct = true) { std::cout << (is_correct ? "YES\n" : "NO\n"); }
void NO(bool is_not_correct = true) { YES(!is_not_correct); }
void Takahashi(bool is_correct = true) { std::cout << (is_correct ? "Takahashi" : "Aoki") << '\n'; }
void Aoki(bool is_not_correct = true) { Takahashi(!is_not_correct); }
namespace internal {
struct graph_csr {
private:
struct edge_list {
using const_iterator = std::vector<int>::const_iterator;
edge_list(const graph_csr &g, int v) : g(g), v(v) {}
const_iterator begin() const { return std::next(g.elist.begin(), g.start[v]); }
const_iterator end() const { return std::next(g.elist.begin(), g.start[v + 1]); }
private:
const graph_csr &g;
int v;
};
public:
graph_csr(int n) : _size(n), edges(), start(n + 1) {}
edge_list operator[](int i) const { return edge_list(*this, i); }
constexpr int size() const { return _size; }
void build() {
for (auto [u, v] : edges) ++start[u + 1];
for (int i = 0; i < _size; ++i) start[i + 1] += start[i];
auto counter = start;
elist = std::vector<int>(edges.size());
for (auto [u, v] : edges) elist[counter[u]++] = v;
}
void add_edge(int u, int v) { edges.emplace_back(u, v); }
void add_edges(int u, int v) {
edges.emplace_back(u, v);
edges.emplace_back(v, u);
}
void input_edge(int m, int base = 1) {
for (int i = 0; i < m; ++i) {
int from, to;
std::cin >> from >> to;
add_edge(from - base, to - base);
}
build();
}
void input_edges(int m, int base = 1) {
for (int i = 0; i < m; ++i) {
int from, to;
std::cin >> from >> to;
add_edges(from - base, to - base);
}
build();
}
int _size;
std::vector<std::pair<int, int>> edges;
std::vector<int> elist;
std::vector<int> start;
};
} // namespace internal
/**
* @brief HL分解
* @see https://beet-aizu.github.io/library/tree/heavylightdecomposition.cpp
*/
struct heavy_light_decomposition {
heavy_light_decomposition() = default;
template <class T>
heavy_light_decomposition(const Graph<T> &g, int r = 0) : heavy_light_decomposition(g.size()) {
std::vector<int> heavy_path(_size, -1), sub_size(_size, 1);
std::stack<int> st;
st.emplace(r);
int pos = 0;
while (!st.empty()) {
int v = st.top();
st.pop();
vid[pos++] = v;
for (auto &e : g[v]) {
int u = e.to();
if (u == par[v]) continue;
par[u] = v, dep[u] = dep[v] + 1, st.emplace(u);
}
}
for (int i = _size - 1; i >= 0; --i) {
int v = vid[i];
int max_sub = 0;
for (auto &e : g[v]) {
int u = e.to();
if (u == par[v]) continue;
sub_size[v] += sub_size[u];
if (max_sub < sub_size[u]) max_sub = sub_size[u], heavy_path[v] = u;
}
}
nxt[r] = r;
pos = 0;
st.emplace(r);
while (!st.empty()) {
int v = st.top();
st.pop();
vid[v] = pos++;
inv[vid[v]] = v;
int hp = heavy_path[v];
for (auto &e : g[v]) {
int u = e.to();
if (u == par[v] || u == hp) continue;
nxt[u] = u, st.emplace(u);
}
if (hp != -1) nxt[hp] = nxt[v], st.emplace(hp);
}
}
heavy_light_decomposition(const internal::graph_csr &g, int r = 0)
: heavy_light_decomposition(g.size()) {
std::vector<int> heavy_path(_size, -1), sub_size(_size, 1);
std::stack<int> st;
st.emplace(r);
int pos = 0;
while (!st.empty()) {
int v = st.top();
st.pop();
vid[pos++] = v;
for (int u : g[v]) {
if (u == par[v]) continue;
par[u] = v, dep[u] = dep[v] + 1, st.emplace(u);
}
}
for (int i = _size - 1; i >= 0; --i) {
int v = vid[i];
int max_sub = 0;
for (int u : g[v]) {
if (u == par[v]) continue;
sub_size[v] += sub_size[u];
if (max_sub < sub_size[u]) max_sub = sub_size[u], heavy_path[v] = u;
}
}
nxt[r] = r;
pos = 0;
st.emplace(r);
while (!st.empty()) {
int v = st.top();
st.pop();
vid[v] = pos++;
inv[vid[v]] = v;
int hp = heavy_path[v];
for (int u : g[v]) {
if (u == par[v] || u == hp) continue;
nxt[u] = u, st.emplace(u);
}
if (hp != -1) nxt[hp] = nxt[v], st.emplace(hp);
}
}
constexpr int size() const { return _size; }
int get(int v) const { return vid[v]; }
int get_parent(int v) const { return par[v]; }
int get_depth(int v) const { return dep[v]; }
int dist(int u, int v) const {
int d = 0;
while (true) {
if (vid[u] > vid[v]) std::swap(u, v);
if (nxt[u] == nxt[v]) return d + vid[v] - vid[u];
d += vid[v] - vid[nxt[v]] + 1;
v = par[nxt[v]];
}
}
int jump(int u, int v, int k) const {
int d = dist(u, v);
if (d < k) return -1;
int l = lca(u, v);
if (dist(u, l) >= k) return la(u, k);
else return la(v, d - k);
}
int la(int v, int k) const {
while (true) {
int u = nxt[v];
if (vid[v] - k >= vid[u]) return inv[vid[v] - k];
k -= vid[v] - vid[u] + 1;
v = par[u];
}
}
int lca(int u, int v) const {
while (true) {
if (vid[u] > vid[v]) std::swap(u, v);
if (nxt[u] == nxt[v]) return u;
v = par[nxt[v]];
}
}
template <class F>
void for_each(int u, int v, const F &f) const {
while (true) {
if (vid[u] > vid[v]) std::swap(u, v);
f(std::max(vid[nxt[v]], vid[u]), vid[v] + 1);
if (nxt[u] != nxt[v]) v = par[nxt[v]];
else break;
}
}
template <class F>
void for_each_edge(int u, int v, const F &f) const {
while (true) {
if (vid[u] > vid[v]) std::swap(u, v);
if (nxt[u] != nxt[v]) {
f(vid[nxt[v]], vid[v] + 1);
v = par[nxt[v]];
} else {
if (u != v) f(vid[u] + 1, vid[v] + 1);
break;
}
}
}
private:
int _size;
std::vector<int> vid, nxt, par, dep, inv;
heavy_light_decomposition(int n) : _size(n), vid(n, -1), nxt(n), par(n, -1), dep(n), inv(n) {}
};
using Mint = modint107;
struct S {
Mint x, y;
S operator+(const S &rhs) const {
return S{x + rhs.x, y + rhs.y};
}
};
struct F {
Mint x;
F operator+(const F &rhs) const {
return F{x + rhs.x};
}
S operator+(const S &rhs) const {
return S{rhs.x + x * rhs.y, rhs.y};
}
};
int main(void) {
int n;
cin >> n;
vector<int> s(n), c(n);
cin >> s >> c;
Graph<void> g(n);
g.input_edges(n - 1);
heavy_light_decomposition hld(g);
vector<S> v(n);
rep (i, n) v[hld.get(i)] = {s[i], c[i]};
lazy_segment_tree<Add<S>, Add<F>> seg(v);
int q;
cin >> q;
while (q--) {
int t;
cin >> t;
if (t == 0) {
int x, y, z;
cin >> x >> y >> z;
--x, --y;
auto f = [&](int u, int v) {
seg.apply(u, v, F{z});
};
hld.for_each(x, y, f);
} else {
int x, y;
cin >> x >> y;
--x, --y;
Mint ans = 0;
auto f = [&](int u, int v) {
ans += seg.prod(u, v).x;
};
hld.for_each(x, y, f);
co(ans);
}
}
return 0;
}