結果

問題 No.2733 Just K-times TSP
ユーザー shogo314
提出日時 2024-04-19 22:18:34
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,518 ms / 2,000 ms
コード長 47,384 bytes
コンパイル時間 2,967 ms
コンパイル使用メモリ 213,896 KB
最終ジャッジ日時 2025-02-21 04:31:40
ジャッジサーバーID
(参考情報)
judge2 / judge3
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 2
other AC * 32
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#line 2 "/home/shogo314/cpp_include/ou-library/graph.hpp"
#include <iostream>
#include <limits>
#include <queue>
#include <vector>
/**
* @brief
*
* @tparam Cost
*/
template <typename Cost=int>
struct Graph {
/**
* @brief
*
* operator int()intdst
*
* for (auto& e : g[v]) v
* for (int dst : g[v]) v
*/
struct Edge {
int src; //!<
int dst; //!<
Cost cost; //!<
int id; //!< (id2)
Edge() = default;
Edge(int src, int dst, Cost cost=1, int id=-1) : src(src), dst(dst), cost(cost), id(id) {}
operator int() const { return dst; }
};
int n; //!<
int m; //!<
std::vector<std::vector<Edge>> g; //!<
/**
* @brief
*/
Graph() : n(0), m(0), g(0) {}
/**
* @brief
* @param n
*/
explicit Graph(int n) : n(n), m(0), g(n) {}
/**
* @brief
* @param u
* @param v
* @param w 1
*/
void add_edge(int u, int v, Cost w=1) {
g[u].push_back({u, v, w, m});
g[v].push_back({v, u, w, m++});
}
/**
* @brief
* @param u
* @param v
* @param w 1
*/
void add_directed_edge(int u, int v, Cost w=1) {
g[u].push_back({u, v, w, m++});
}
/**
* @brief
* @param m
* @param padding -1
* @param weighted false1
* @param directed false
*/
void read(int m, int padding=-1, bool weighted=false, bool directed=false) {
for(int i = 0; i < m; i++) {
int u, v; std::cin >> u >> v; u += padding, v += padding;
Cost c(1);
if(weighted) std::cin >> c;
if(directed) add_directed_edge(u, v, c);
else add_edge(u, v, c);
}
}
/**
* @brief
* @param v
* @return std::vector<Edge>& v
*/
std::vector<Edge>& operator[](int v) {
return g[v];
}
/**
* @brief
* @param v
* @return const std::vector<Edge>& v
*/
const std::vector<Edge>& operator[](int v) const {
return g[v];
}
/**
* @brief
* @return std::vector<Edge> (id)
*
* 1
*/
std::vector<Edge> edges() const {
std::vector<Edge> res(m);
for(int i = 0; i < n; i++) {
for(auto& e : g[i]) {
res[e.id] = e;
}
}
return res;
}
/**
* @brief
*
* @param s
* @param weighted 1 true
* @param inf min inf -1
* @return std::pair<std::vector<Cost>, std::vector<Edge>> first: second:
*/
std::pair<std::vector<Cost>, std::vector<Edge>> shortest_path(int s, bool weignted = true, Cost inf = -1) const {
if(weignted) return shortest_path_dijkstra(s, inf);
return shortest_path_bfs(s, inf);
}
std::vector<int> topological_sort() {
std::vector<int> indeg(n), sorted;
std::queue<int> q;
for (int i = 0; i < n; i++) {
for (int dst : g[i]) indeg[dst]++;
}
for (int i = 0; i < n; i++) {
if (!indeg[i]) q.push(i);
}
while (!q.empty()) {
int cur = q.front(); q.pop();
for (int dst : g[cur]) {
if (!--indeg[dst]) q.push(dst);
}
sorted.push_back(cur);
}
return sorted;
}
private:
std::pair<std::vector<Cost>, std::vector<Edge>> shortest_path_bfs(int s, Cost inf) const {
std::vector<Cost> dist(n, inf);
std::vector<Edge> prev(n);
std::queue<int> que;
dist[s] = 0;
que.push(s);
while(!que.empty()) {
int u = que.front(); que.pop();
for(auto& e : g[u]) {
if(dist[e.dst] == inf) {
dist[e.dst] = dist[e.src] + 1;
prev[e.dst] = e;
que.push(e.dst);
}
}
}
return {dist, prev};
}
std::pair<std::vector<Cost>, std::vector<Edge>> shortest_path_dijkstra(int s, Cost inf) const {
std::vector<Cost> dist(n, inf);
std::vector<Edge> prev(n);
using Node = std::pair<Cost, int>;
std::priority_queue<Node, std::vector<Node>, std::greater<Node>> que;
dist[s] = 0;
que.push({0, s});
while(!que.empty()) {
auto [d, u] = que.top(); que.pop();
if(d > dist[u]) continue;
for(auto& e : g[u]) {
if(dist[e.dst] == inf || dist[e.dst] > dist[e.src] + e.cost) {
dist[e.dst] = dist[e.src] + e.cost;
prev[e.dst] = e;
que.push({dist[e.dst], e.dst});
}
}
}
return {dist, prev};
}
};
#line 2 "/home/shogo314/cpp_include/ou-library/modint.hpp"
/**
* @file modint.hpp
* @brief mod
*/
#line 9 "/home/shogo314/cpp_include/ou-library/modint.hpp"
#include <utility>
#line 11 "/home/shogo314/cpp_include/ou-library/modint.hpp"
#include <type_traits>
#include <cstdint>
#include <cassert>
namespace detail {
static constexpr std::uint16_t prime32_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,
};
static constexpr bool is_SPRP(std::uint32_t n, std::uint32_t a) noexcept {
std::uint32_t d = n - 1;
std::uint32_t s = 0;
while ((d & 1) == 0) {
++s;
d >>= 1;
}
std::uint64_t cur = 1;
std::uint64_t pw = d;
while (pw) {
if (pw & 1) cur = (cur * a) % n;
a = (static_cast<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;
}
// 32
// : M. Forisek and J. Jancina, “Fast Primality Testing for Integers That Fit into a Machine Word,” presented at the Conference on Current
        Trends in Theory and Practice of Informatics, 2015.
[[nodiscard]]
static constexpr bool is_prime32(std::uint32_t x) noexcept {
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) & 0xff;
return is_SPRP(x, prime32_bases[h]);
}
}
/// @brief static_modint dynamic_modint CRTP
/// @tparam Modint
template <class Modint>
class modint_base {
public:
/// @brief
using value_type = std::uint32_t;
/// @brief 0
constexpr modint_base() noexcept
: m_value{ 0 } {}
/// @brief @c value
/// @param value 使
template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral> && std::is_signed_v<SignedIntegral>>* = nullptr>
constexpr modint_base(SignedIntegral value) noexcept
: m_value{ static_cast<value_type>((static_cast<long long>(value) % Modint::mod() + Modint::mod()) % Modint::mod()) } {}
/// @brief @c value
/// @param value 使
template <class UnsignedIntegral, std::enable_if_t<std::is_integral_v<UnsignedIntegral> && std::is_unsigned_v<UnsignedIntegral>>* = nullptr>
constexpr modint_base(UnsignedIntegral value) noexcept
: m_value{ static_cast<value_type>(value % Modint::mod()) } {}
/// @brief
/// @return
[[nodiscard]]
constexpr value_type value() const noexcept {
return m_value;
}
/// @brief
/// @return @c *this
constexpr Modint& operator++() noexcept {
++m_value;
if (m_value == Modint::mod()) {
m_value = 0;
}
return static_cast<Modint&>(*this);
}
/// @brief
/// @return @c *this
constexpr Modint operator++(int) noexcept {
auto x = static_cast<const Modint&>(*this);
++*this;
return x;
}
/// @brief
/// @return @c *this
constexpr Modint& operator--() noexcept {
if (m_value == 0) {
m_value = Modint::mod();
}
--m_value;
return static_cast<Modint&>(*this);
}
/// @brief
/// @return @c *this
constexpr Modint operator--(int) noexcept {
auto x = static_cast<const Modint&>(*this);
--*this;
return x;
}
/// @brief @c x
/// @param x
/// @return @c *this
constexpr Modint& operator+=(const Modint& x) noexcept {
m_value += x.m_value;
if (m_value >= Modint::mod()) {
m_value -= Modint::mod();
}
return static_cast<Modint&>(*this);
}
/// @brief @c x
/// @param x
/// @return @c *this
constexpr Modint& operator-=(const Modint& x) noexcept {
m_value -= x.m_value;
if (m_value >= Modint::mod()) {
m_value += Modint::mod();
}
return static_cast<Modint&>(*this);
}
/// @brief @c x
/// @param x
/// @return @c *this
constexpr Modint& operator*=(const Modint& x) noexcept {
m_value = static_cast<value_type>(static_cast<std::uint64_t>(m_value) * x.m_value % Modint::mod());
return static_cast<Modint&>(*this);
}
/// @brief @c x
/// @remark @f$O(\log x)@f$
/// @param x
/// @return @c *this
constexpr Modint& operator/=(const Modint& x) noexcept {
return *this *= x.inv();
}
/// @brief
/// @return @c *this
[[nodiscard]]
constexpr Modint operator+() const noexcept {
return static_cast<const Modint&>(*this);
}
/// @brief
/// @return
[[nodiscard]]
constexpr Modint operator-() const noexcept {
return 0 - static_cast<const Modint&>(*this);
}
/// @brief @c n
/// @remark @f$O(\log n)@f$
/// @param n
/// @return @c n
[[nodiscard]]
constexpr Modint pow(unsigned long long n) const noexcept {
Modint x = 1;
Modint y = static_cast<const Modint&>(*this);
while (n) {
if (n & 1) {
x *= y;
}
y *= y;
n >>= 1;
}
return x;
}
/// @brief
/// @remark @f$O(\log value)@f$
/// @return
[[nodiscard]]
constexpr Modint inv() const noexcept {
long long a = Modint::mod();
long long b = m_value;
long long x = 0;
long long y = 1;
while (b) {
auto t = a / b;
auto u = a - t * b;
a = b;
b = u;
u = x - t * y;
x = y;
y = u;
}
assert(a == 1 && "The inverse element does not exist.");
x %= Modint::mod();
if (x < 0) {
x += Modint::mod();
}
return x;
}
/// @brief @c x @c y
/// @param x
/// @param y
/// @return @c x @c y
[[nodiscard]]
friend constexpr Modint operator+(const Modint& x, const Modint& y) noexcept {
return std::move(Modint{ x } += y);
}
/// @brief @c x @c y
/// @param x
/// @param y
/// @return @c x @c y
[[nodiscard]]
friend constexpr Modint operator-(const Modint& x, const Modint& y) noexcept {
return std::move(Modint{ x } -= y);
}
/// @brief @c x @c y
/// @param x
/// @param y
/// @return @c x @c y
[[nodiscard]]
friend constexpr Modint operator*(const Modint& x, const Modint& y) noexcept {
return std::move(Modint{ x } *= y);
}
/// @brief @c x @c y
/// @param x
/// @param y
/// @return @c x @c y
[[nodiscard]]
friend constexpr Modint operator/(const Modint& x, const Modint& y) noexcept {
return std::move(Modint{ x } /= y);
}
/// @brief @c x @c y 調
/// @return @c x @c y @c true @c false
[[nodiscard]]
friend constexpr bool operator==(const Modint& x, const Modint& y) noexcept {
return x.m_value == y.m_value;
}
/// @brief @c x @c y 調
/// @return @c x @c y @c false @c true
[[nodiscard]]
friend constexpr bool operator!=(const Modint& x, const Modint& y) noexcept {
return not (x == y);
}
/// @brief @c x
/// @tparam CharT
/// @tparam Traits
/// @param is
/// @param x
/// @return @c is
template <class CharT, class Traits>
friend std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, Modint& x) {
long long tmp;
is >> tmp;
x = tmp;
return is;
}
/// @brief @c x
/// @tparam CharT
/// @tparam Traits
/// @param os
/// @param x
/// @return @c os
template <class CharT, class Traits>
friend std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const Modint& x) {
os << x.value();
return os;
}
protected:
value_type m_value;
};
/// @brief mod
/// @tparam Mod
template <std::uint32_t Mod>
class static_modint : public modint_base<static_modint<Mod>> {
static_assert(Mod > 0 && Mod <= std::numeric_limits<std::uint32_t>::max() / 2);
private:
using base_type = modint_base<static_modint<Mod>>;
public:
using typename base_type::value_type;
/// @brief
/// @return
[[nodiscard]]
static constexpr value_type mod() noexcept {
return Mod;
}
/// @brief 0
constexpr static_modint() noexcept
: base_type{} {}
/// @brief @c value
/// @param value 使
template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral>>* = nullptr>
constexpr static_modint(SignedIntegral value) noexcept
: base_type{value} {}
/// @brief
/// @remark @f$O(\log value)@f$
/// @return
[[nodiscard]]
constexpr static_modint inv() const noexcept {
if constexpr (detail::is_prime32(Mod)) {
assert(this->m_value != 0 && "The inverse element of zero does not exist.");
return this->pow(Mod - 2);
}
else {
return base_type::inv();
}
}
};
/// @brief mod
/// @tparam ID ID
template <int ID>
class dynamic_modint : public modint_base<dynamic_modint<ID>> {
private:
using base_type = modint_base<dynamic_modint<ID>>;
public:
using typename base_type::value_type;
/// @brief
/// @return
[[nodiscard]]
static value_type mod() noexcept {
return modulus;
}
/// @brief
/// @param m
static void set_mod(value_type m) noexcept {
assert(m > 0 && m <= std::numeric_limits<value_type>::max() / 2);
modulus = m;
}
/// @brief 0
constexpr dynamic_modint() noexcept
: base_type{} {}
/// @brief @c value
/// @param value 使
template <class SignedIntegral, std::enable_if_t<std::is_integral_v<SignedIntegral>>* = nullptr>
constexpr dynamic_modint(SignedIntegral value) noexcept
: base_type{value} {}
private:
inline static value_type modulus = 998244353;
};
using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;
#line 2 "/home/shogo314/cpp_include/sh-library/base/all"
#include <bits/stdc++.h>
#line 5 "/home/shogo314/cpp_include/sh-library/base/container_func.hpp"
#include <initializer_list>
#line 4 "/home/shogo314/cpp_include/sh-library/base/traits.hpp"
#define HAS_METHOD(func_name) \
namespace detail { \
template <class T, class = void> \
struct has_##func_name##_impl : std::false_type {}; \
template <class T> \
struct has_##func_name##_impl<T, std::void_t<decltype(std::declval<T>().func_name())>> \
: std::true_type {}; \
} \
template <class T> \
struct has_##func_name : detail::has_##func_name##_impl<T>::type {}; \
template <class T> \
inline constexpr bool has_##func_name##_v = has_##func_name<T>::value;
#define HAS_METHOD_ARG(func_name) \
namespace detail { \
template <class T, typename U, class = void> \
struct has_##func_name##_impl : std::false_type {}; \
template <class T, typename U> \
struct has_##func_name##_impl<T, U, std::void_t<decltype(std::declval<T>().func_name(std::declval<U>()))>> \
: std::true_type {}; \
} \
template <class T, typename U> \
struct has_##func_name : detail::has_##func_name##_impl<T, U>::type {}; \
template <class T, typename U> \
inline constexpr bool has_##func_name##_v = has_##func_name<T, U>::value;
HAS_METHOD(repr)
HAS_METHOD(type_str)
HAS_METHOD(initializer_str)
HAS_METHOD(max)
HAS_METHOD(min)
HAS_METHOD(reversed)
HAS_METHOD(sorted)
HAS_METHOD(sum)
HAS_METHOD(product)
HAS_METHOD(product_xor)
HAS_METHOD_ARG(count)
HAS_METHOD_ARG(find)
HAS_METHOD_ARG(lower_bound)
HAS_METHOD_ARG(upper_bound)
#define ENABLE_IF_T_IMPL(expr) std::enable_if_t<expr, std::nullptr_t> = nullptr
#define ENABLE_IF_T(...) ENABLE_IF_T_IMPL((__VA_ARGS__))
template <class C>
using mem_value_type = typename C::value_type;
template <class C>
using mem_difference_type = typename C::difference_type;
#line 9 "/home/shogo314/cpp_include/sh-library/base/container_func.hpp"
#define METHOD_EXPAND(func_name) \
template <typename T, ENABLE_IF_T(has_##func_name##_v<T>)> \
inline constexpr auto func_name(const T &t) -> decltype(t.func_name()) { \
return t.func_name(); \
}
#define METHOD_AND_FUNC_ARG_EXPAND(func_name) \
template <typename T, typename U, ENABLE_IF_T(has_##func_name##_v<T, U>)> \
inline constexpr auto func_name(const T &t, const U &u) \
-> decltype(t.func_name(u)) { \
return t.func_name(u); \
} \
template <typename T, typename U, ENABLE_IF_T(not has_##func_name##_v<T, U>)> \
inline constexpr auto func_name(const T &t, const U &u) \
-> decltype(std::func_name(t.begin(), t.end(), u)) { \
return std::func_name(t.begin(), t.end(), u); \
}
METHOD_EXPAND(reversed)
template <class C, ENABLE_IF_T(not has_reversed_v<C>)>
inline constexpr C reversed(C t) {
std::reverse(t.begin(), t.end());
return t;
}
METHOD_EXPAND(sorted)
template <class C, ENABLE_IF_T(not has_sorted_v<C>)>
inline constexpr C sorted(C t) {
std::sort(t.begin(), t.end());
return t;
}
template <class C, class F, ENABLE_IF_T(not has_sorted_v<C> and std::is_invocable_r_v<bool, F, mem_value_type<C>, mem_value_type<C>>)>
inline constexpr C sorted(C t, F f) {
std::sort(t.begin(), t.end(), f);
return t;
}
template <class C>
inline constexpr void sort(C &t) {
std::sort(t.begin(), t.end());
}
template <class C, class F, ENABLE_IF_T(std::is_invocable_r_v<bool, F, mem_value_type<C>, mem_value_type<C>>)>
inline constexpr void sort(C &t, F f) {
std::sort(t.begin(), t.end(), f);
}
template <class C, class F, ENABLE_IF_T(std::is_invocable_v<F, mem_value_type<C>>)>
inline constexpr void sort_by_key(C &t, F f) {
std::sort(t.begin(), t.end(), [&](const mem_value_type<C> &left, const mem_value_type<C> &right) {
return f(left) < f(right);
});
}
template <class C>
inline constexpr void reverse(C &t) {
std::reverse(t.begin(), t.end());
}
METHOD_EXPAND(max)
template <class C, ENABLE_IF_T(not has_max_v<C>)>
inline constexpr mem_value_type<C> max(const C &v) {
assert(v.begin() != v.end());
return *std::max_element(v.begin(), v.end());
}
template <typename T>
inline constexpr T max(const std::initializer_list<T> &v) {
return std::max(v);
}
METHOD_EXPAND(min)
template <class C, ENABLE_IF_T(not has_max_v<C>)>
inline constexpr mem_value_type<C> min(const C &v) {
assert(v.begin() != v.end());
return *std::min_element(v.begin(), v.end());
}
template <typename T>
inline constexpr T min(const std::initializer_list<T> &v) {
return std::min(v);
}
METHOD_EXPAND(sum)
template <class C, ENABLE_IF_T(not has_sum_v<C>)>
inline constexpr mem_value_type<C> sum(const C &v) {
return std::accumulate(v.begin(), v.end(), mem_value_type<C>{});
}
template <typename T>
inline constexpr T sum(const std::initializer_list<T> &v) {
return std::accumulate(v.begin(), v.end(), T{});
}
METHOD_EXPAND(product)
template <class C, ENABLE_IF_T(not has_product_v<C>)>
inline constexpr mem_value_type<C> product(const C &v) {
return std::accumulate(v.begin(), v.end(), mem_value_type<C>{1}, std::multiplies<mem_value_type<C>>());
}
template <typename T>
inline constexpr T product(const std::initializer_list<T> &v) {
return std::accumulate(v.begin(), v.end(), T{1}, std::multiplies<T>());
}
METHOD_EXPAND(product_xor)
template <class C, ENABLE_IF_T(not has_product_xor_v<C>)>
inline constexpr mem_value_type<C> product_xor(const C &v) {
return std::accumulate(v.begin(), v.end(), mem_value_type<C>{0}, std::bit_xor<mem_value_type<C>>());
}
template <typename T>
inline constexpr T product_xor(const std::initializer_list<T> &v) {
return std::accumulate(v.begin(), v.end(), T{0}, std::bit_xor<T>());
}
template <class C>
inline constexpr mem_value_type<C> maximum_subarray(const C &v) {
assert(not v.empty());
auto itr = v.begin();
mem_value_type<C> tmp = *itr++;
mem_value_type<C> res = tmp;
while (itr != v.end()) {
tmp += *itr;
if (tmp < *itr) tmp = *itr;
if (res < tmp) res = tmp;
++itr;
}
return res;
}
template <class C>
inline constexpr mem_value_type<C> maximum_subarray(const C &v, mem_value_type<C> init) {
mem_value_type<C> res = init, tmp = init;
for (const auto &a : v) {
tmp += a;
if (tmp < init) tmp = init;
if (res < tmp) res = tmp;
}
return res;
}
METHOD_AND_FUNC_ARG_EXPAND(count)
METHOD_AND_FUNC_ARG_EXPAND(find)
METHOD_AND_FUNC_ARG_EXPAND(lower_bound)
METHOD_AND_FUNC_ARG_EXPAND(upper_bound)
template <class C, typename T>
inline constexpr bool contains(const C &c, const T &t) {
return find(c, t) != c.end();
}
template <class C>
inline constexpr mem_value_type<C> gcd(const C &v) {
mem_value_type<C> init(0);
for (const auto &e : v) init = std::gcd(init, e);
return init;
}
template <class C>
inline constexpr mem_value_type<C> average(const C &v) {
assert(v.size());
return sum(v) / v.size();
}
template <class C>
inline constexpr mem_value_type<C> median(const C &v) {
assert(not v.empty());
std::vector<size_t> u(v.size());
std::iota(u.begin(), u.end(), 0);
std::sort(u.begin(), u.end(), [&](size_t a, size_t b) {
return v[a] < v[b];
});
if (v.size() & 1) {
return v[u[v.size() / 2]];
}
// C++20
// return std::midpoint(v[u[v.size() / 2]], v[u[v.size() / 2 - 1]]);
return (v[u[v.size() / 2]] + v[u[v.size() / 2 - 1]]) / 2;
}
template <class C, typename U>
inline constexpr std::ptrdiff_t index(const C &v, const U &x) {
return std::distance(v.begin(), find(v, x));
}
template <class C, ENABLE_IF_T(std::is_integral_v<mem_value_type<C>>)>
inline constexpr mem_value_type<C> mex(const C &v) {
std::vector<bool> b(v.size() + 1);
for (const auto &a : v) {
if (0 <= a and a < b.size()) {
b[a] = true;
}
}
mem_value_type<C> ret;
for (size_t i = 0; i < b.size(); i++) {
if (not b[i]) {
ret = i;
break;
}
}
return ret;
}
template <class C>
inline constexpr mem_difference_type<C> bisect_left(const C &v, const mem_value_type<C> &x) {
return std::distance(v.begin(), lower_bound(v, x));
}
template <class C>
inline constexpr mem_difference_type<C> bisect_right(const C &v, const mem_value_type<C> &x) {
return std::distance(v.begin(), upper_bound(v, x));
}
#line 6 "/home/shogo314/cpp_include/sh-library/base/functions.hpp"
template <typename T1, typename T2>
inline constexpr bool chmin(T1 &a, T2 b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template <typename T1, typename T2>
inline constexpr bool chmax(T1 &a, T2 b) {
if (a < b) {
a = b;
return true;
}
return false;
}
inline constexpr long long max(const long long &t1, const long long &t2) {
return std::max<long long>(t1, t2);
}
inline constexpr long long min(const long long &t1, const long long &t2) {
return std::min<long long>(t1, t2);
}
using std::abs;
using std::gcd;
using std::lcm;
using std::size;
template <typename T>
constexpr T extgcd(const T &a, const T &b, T &x, T &y) {
T d = a;
if (b != 0) {
d = extgcd(b, a % b, y, x);
y -= (a / b) * x;
} else {
x = 1;
y = 0;
}
return d;
}
template <typename M, typename N, class F, ENABLE_IF_T(std::is_integral_v<std::common_type_t<M, N>> and std::is_invocable_r_v<bool, F, std
    ::common_type_t<M, N>>)>
inline constexpr std::common_type_t<M, N> binary_search(const M &ok, const N &ng, F f) {
std::common_type_t<M, N> _ok = ok, _ng = ng;
assert(f(_ok));
while (std::abs(_ok - _ng) > 1) {
std::common_type_t<M, N> mid = (_ok + _ng) / 2;
if (f(mid)) {
_ok = mid;
} else {
_ng = mid;
}
}
return _ok;
}
template <typename M, typename N, class F, ENABLE_IF_T(not std::is_integral_v<std::common_type_t<M, N>> and std::is_invocable_r_v<bool, F, std
    ::common_type_t<M, N>>)>
inline constexpr std::common_type_t<M, N> binary_search(const M &ok, const N &ng, F f) {
std::common_type_t<M, N> _ok = ok, _ng = ng;
assert(f(_ok));
for (int i = 0; i < 100; i++) {
std::common_type_t<M, N> mid = (_ok + _ng) / 2;
if (f(mid)) {
_ok = mid;
} else {
_ng = mid;
}
}
return _ok;
}
/**
* 0 <= x < a
*/
inline constexpr bool inrange(long long x, long long a) {
return 0 <= x and x < a;
}
/**
* a <= x < b
*/
inline constexpr bool inrange(long long x, long long a, long long b) {
return a <= x and x < b;
}
/**
* 0 <= x < a and 0 <= y < b
*/
inline constexpr bool inrect(long long x, long long y, long long a, long long b) {
return 0 <= x and x < a and 0 <= y and y < b;
}
#line 8 "/home/shogo314/cpp_include/sh-library/base/io.hpp"
namespace tuple_io {
template <typename Tuple, size_t I, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& read_tuple(std::basic_istream<CharT, Traits>& is, Tuple& t) {
is >> std::get<I>(t);
if constexpr (I + 1 < std::tuple_size_v<Tuple>) {
return read_tuple<Tuple, I + 1>(is, t);
}
return is;
}
template <typename Tuple, size_t I, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& write_tuple(std::basic_ostream<CharT, Traits>& os, const Tuple& t) {
os << std::get<I>(t);
if constexpr (I + 1 < std::tuple_size_v<Tuple>) {
os << CharT(' ');
return write_tuple<Tuple, I + 1>(os, t);
}
return os;
}
}; // namespace tuple_io
template <typename T1, typename T2, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::pair<T1, T2>& p) {
is >> p.first >> p.second;
return is;
}
template <typename... Types, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::tuple<Types...>& p) {
return tuple_io::read_tuple<std::tuple<Types...>, 0>(is, p);
}
template <typename T, size_t N, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::array<T, N>& a) {
for (auto& e : a) is >> e;
return is;
}
template <typename T, typename CharT, typename Traits>
std::basic_istream<CharT, Traits>& operator>>(std::basic_istream<CharT, Traits>& is, std::vector<T>& v) {
for (auto& e : v) is >> e;
return is;
}
template <typename T1, typename T2, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::pair<T1, T2>& p) {
os << p.first << CharT(' ') << p.second;
return os;
}
template <typename... Types, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::tuple<Types...>& p) {
return tuple_io::write_tuple<std::tuple<Types...>, 0>(os, p);
}
template <typename T, size_t N, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::array<T, N>& a) {
for (size_t i = 0; i < N; ++i) {
if (i) os << CharT(' ');
os << a[i];
}
return os;
}
template <typename T, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::vector<T>& v) {
for (size_t i = 0; i < v.size(); ++i) {
if (i) os << CharT(' ');
os << v[i];
}
return os;
}
template <typename T, typename CharT, typename Traits>
std::basic_ostream<CharT, Traits>& operator<<(std::basic_ostream<CharT, Traits>& os, const std::set<T>& s) {
for (auto itr = s.begin(); itr != s.end(); ++itr) {
if (itr != s.begin()) os << CharT(' ');
os << *itr;
}
return os;
}
/**
* @brief
*/
void print() { std::cout << '\n'; }
/**
* @brief
*
* @tparam T
* @param x
*/
template <typename T>
void print(const T& x) { std::cout << x << '\n'; }
/**
* @brief
*
* @tparam T 1
* @tparam Tail 2
* @param x 1
* @param tail 2
*/
template <typename T, typename... Tail>
void print(const T& x, const Tail&... tail) {
std::cout << x << ' ';
print(tail...);
}
/**
* @brief
*/
void err() { std::cerr << std::endl; }
/**
* @brief
*
* @tparam T
* @param x
*/
template <typename T>
void err(const T& x) { std::cerr << x << std::endl; }
/**
* @brief
*
* @tparam T 1
* @tparam Tail 2
* @param x 1
* @param tail 2
*/
template <typename T, typename... Tail>
void err(const T& x, const Tail&... tail) {
std::cerr << x << ' ';
err(tail...);
}
#line 3 "/home/shogo314/cpp_include/sh-library/base/type_alias.hpp"
using ll = long long;
using ull = unsigned long long;
using ld = long double;
template <typename T>
using vec = std::vector<T>;
template <typename T, int N>
using ary = std::array<T, N>;
using str = std::string;
using std::deque;
using std::list;
using std::map;
using std::pair;
using std::set;
using pl = pair<ll, ll>;
using pd = pair<ld, ld>;
template <typename T>
using vv = vec<vec<T>>;
template <typename T>
using vvv = vec<vec<vec<T>>>;
using vl = vec<ll>;
using vvl = vv<ll>;
using vvvl = vvv<ll>;
using vs = vec<str>;
using vc = vec<char>;
using vi = vec<int>;
using vb = vec<bool>;
template <typename T1, typename T2>
using vp = vec<pair<T1, T2>>;
using vpl = vec<pl>;
using vvpl = vv<pl>;
using vd = vec<ld>;
using vpd = vec<pd>;
template <int N>
using al = ary<ll, N>;
template <int N1, int N2>
using aal = ary<ary<ll, N2>, N1>;
template <int N>
using val = vec<al<N>>;
template <int N>
using avl = ary<vl,N>;
template <typename T>
using ml = std::map<ll, T>;
using mll = std::map<ll, ll>;
using sl = std::set<ll>;
using spl = set<pl>;
template <int N>
using sal = set<al<N>>;
template <int N>
using asl = ary<sl,N>;
template <typename T>
using heap_max = std::priority_queue<T, std::vector<T>, std::less<T>>;
template <typename T>
using heap_min = std::priority_queue<T, std::vector<T>, std::greater<T>>;
#line 3 "/home/shogo314/cpp_include/sh-library/base/macro.hpp"
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#define all(obj) (obj).begin(), (obj).end()
#define repts(i, a, n, t) for (long long i = (a); i < (n); i+=(t))
#define reps(i, a, n) for (long long i = (a); i < (n); i++)
#define rep(i, n) reps(i, 0, (n))
#define rrep(i, n) reps(i, 1, (n) + 1)
#define repds(i, a, n) for (long long i = (n)-1; i >= (a); i--)
#define repd(i, n) repds(i, 0, (n))
#define rrepd(i, n) repds(i, 1, (n) + 1)
#define rep2(i, j, x, y) rep(i, x) rep(j, y)
inline void scan(){}
template<class Head,class... Tail>
inline void scan(Head&head,Tail&... tail){std::cin>>head;scan(tail...);}
#define LL(...) ll __VA_ARGS__;scan(__VA_ARGS__)
#define STR(...) str __VA_ARGS__;scan(__VA_ARGS__)
#define IN(a, x) a x; std::cin >> x;
#define CHAR(x) char x; std::cin >> x;
#define VL(a,n) vl a(n); std::cin >> a;
#define AL(a,k) al<k> a; std::cin >> a;
#define AAL(a,n,m) aal<n,m> a; std::cin >> a;
#define VC(a,n) vc a(n); std::cin >> a;
#define VS(a,n) vs a(n); std::cin >> a;
#define VPL(a,n) vpl a(n); std::cin >> a;
#define VAL(a,n,k) val<k> a(n); std::cin >> a;
#define VVL(a,n,m) vvl a(n,vl(m)); std::cin >> a;
#define SL(a,n) sl a;{VL(b,n);a=sl(all(b));}
#define NO std::cout << "NO" << std::endl; return;
#define YES std::cout << "YES" << std::endl; return;
#define No std::cout << "No" << std::endl; return;
#define Yes std::cout << "Yes" << std::endl; return;
#line 8 "/home/shogo314/cpp_include/sh-library/base/vector_func.hpp"
template <typename T>
std::vector<std::ptrdiff_t> sorted_idx(const std::vector<T> &v) {
std::vector<std::ptrdiff_t> ret(v.size());
std::iota(ret.begin(), ret.end(), 0);
std::sort(ret.begin(), ret.end(), [&](std::ptrdiff_t i, std::ptrdiff_t j) {
return v[i] < v[j];
});
return ret;
}
template <typename T>
inline std::vector<T> &operator++(std::vector<T> &v) {
for (auto &e : v) e++;
return v;
}
template <typename T>
inline std::vector<T> operator++(std::vector<T> &v, int) {
auto res = v;
for (auto &e : v) e++;
return res;
}
template <typename T>
inline std::vector<T> &operator--(std::vector<T> &v) {
for (auto &e : v) e--;
return v;
}
template <typename T>
inline std::vector<T> operator--(std::vector<T> &v, int) {
auto res = v;
for (auto &e : v) e--;
return res;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator+=(std::vector<T> &v1, const std::vector<U> &v2) {
if (v2.size() > v1.size()) {
v1.resize(v2.size());
}
for (size_t i = 0; i < v2.size(); i++) {
v1[i] += v2[i];
}
return v1;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator+(const std::vector<T> &v1, const std::vector<U> &v2) {
std::vector<T> res(v1);
return res += v2;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator+=(std::vector<T> &v, const U &u) {
for (T &e : v) {
e += u;
}
return v;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator+(const std::vector<T> &v, const U &u) {
std::vector<T> res(v);
return res += u;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator+(const U &u, const std::vector<T> &v) {
std::vector<T> res(v);
return res += u;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator*=(std::vector<T> &v1, const std::vector<U> &v2) {
if (v2.size() > v1.size()) {
v1.resize(v2.size());
}
for (size_t i = 0; i < v2.size(); i++) {
v1[i] *= v2[i];
}
for (size_t i = v2.size(); i < v1.size(); i++) {
v1[i] *= U(0);
}
return v1;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator*(const std::vector<T> &v1, const std::vector<U> &v2) {
std::vector<T> res(v1);
return res *= v2;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator*=(std::vector<T> &v, const U &u) {
for (T &e : v) {
e *= u;
}
return v;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator*(const std::vector<T> &v, const U &u) {
std::vector<T> res(v);
return res *= u;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> operator*(const U &u, const std::vector<T> &v) {
std::vector<T> res(v);
return res *= u;
}
template <typename T, typename U>
inline std::vector<T> &assign(std::vector<T> &v1, const std::vector<U> &v2) {
v1.assign(v2.begin(), v2.end());
return v1;
}
template <typename T, typename U>
inline std::vector<T> &extend(std::vector<T> &v1, const std::vector<U> &v2) {
v1.insert(v1.end(), v2.begin(), v2.end());
return v1;
}
template <typename T, typename U, ENABLE_IF_T(std::is_convertible_v<U, T>)>
inline std::vector<T> &operator|=(std::vector<T> &v1, const std::vector<U> &v2) {
return extend(v1, v2);
}
template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>
inline std::vector<T> &operator|=(std::vector<T> &v, const U &u) {
std::vector<T> w(v);
v.clear();
for (int i = 0; i < u; i++) {
extend(v, w);
}
return v;
}
template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>
inline std::vector<T> operator|(const std::vector<T> &v, const U &u) {
std::vector<T> res(v);
return res |= u;
}
template <typename T, typename U, ENABLE_IF_T(std::is_integral_v<U>)>
inline std::vector<T> operator|(const U &u, const std::vector<T> &v) {
std::vector<T> res(v);
return res |= u;
}
template <typename T>
inline std::vector<T> abs(const std::vector<T> &v) {
std::vector<T> ret;
ret.reserve(v.size());
for (const T &e : v) ret.push_back(std::abs(e));
return ret;
}
template <typename T>
std::vector<T> partial_sum(const std::vector<T> &v) {
std::vector<T> ret(v.size());
std::partial_sum(v.begin(), v.end(), ret.begin());
return ret;
}
template <typename T, ENABLE_IF_T(std::is_integral_v<T>)>
std::vector<T> iota(T n) {
assert(n >= 0);
std::vector<T> ret(n);
std::iota(ret.begin(), ret.end(), 0);
return ret;
}
#line 4 "main.cpp"
using mint = modint998244353;
void solve() {
LL(N, M, K);
Graph<> graph(N);
graph.read(M);
vl powk = {1};
rep(_, N) {
powk.push_back(powk.back() * (K + 1));
}
ll MAX = N * powk[N];
vec<mint> dp(MAX);
auto xx = [&](ll a) -> pair<int, vl> {
vl ret(N);
int u = a / powk[N];
a %= powk[N];
rep(i, N) {
ret[i] = a % (K + 1);
a /= K + 1;
}
return {u, ret};
};
auto yy = [&](int u, vl cc) -> ll {
ll s = 0;
repd(i, N) {
s *= K + 1;
s += cc[i];
}
s += powk[N] * u;
return s;
};
rep(i, N) {
vl cc(N);
cc[i]++;
dp[yy(i, cc)] = 1;
}
rep(cc_, powk[N]) {
rep(u, N) {
ll l = cc_ + u * powk[N];
auto [_, cc] = xx(l);
for (int v : graph[u]) {
if (cc[v] == K) continue;
vl dd(cc);
dd[v]++;
dp[yy(v, dd)] += dp[l];
}
}
}
mint ans = 0;
rep(i, N) {
ans += dp[(powk[N] - 1) + i * powk[N]];
}
print(ans);
}
int main() {
std::cin.tie(nullptr);
std::ios_base::sync_with_stdio(false);
solve();
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0