結果
| 問題 | No.2531 Coloring Vertices on Namori |
| ユーザー |
 nok0
|
| 提出日時 | 2023-11-03 22:04:06 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 307 ms / 2,000 ms |
| コード長 | 47,023 bytes |
| コンパイル時間 | 2,875 ms |
| コンパイル使用メモリ | 236,188 KB |
| 実行使用メモリ | 65,028 KB |
| 最終ジャッジ日時 | 2024-09-25 20:24:21 |
| 合計ジャッジ時間 | 10,430 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge3 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 2 ms
6,812 KB |
| testcase_01 | AC | 2 ms
6,816 KB |
| testcase_02 | AC | 2 ms
6,812 KB |
| testcase_03 | AC | 2 ms
6,940 KB |
| testcase_04 | AC | 2 ms
6,944 KB |
| testcase_05 | AC | 116 ms
64,832 KB |
| testcase_06 | AC | 2 ms
6,940 KB |
| testcase_07 | AC | 117 ms
65,028 KB |
| testcase_08 | AC | 233 ms
64,976 KB |
| testcase_09 | AC | 241 ms
65,028 KB |
| testcase_10 | AC | 235 ms
64,956 KB |
| testcase_11 | AC | 87 ms
38,424 KB |
| testcase_12 | AC | 85 ms
37,140 KB |
| testcase_13 | AC | 88 ms
39,388 KB |
| testcase_14 | AC | 194 ms
65,016 KB |
| testcase_15 | AC | 184 ms
65,012 KB |
| testcase_16 | AC | 190 ms
64,964 KB |
| testcase_17 | AC | 2 ms
6,940 KB |
| testcase_18 | AC | 2 ms
6,940 KB |
| testcase_19 | AC | 2 ms
6,940 KB |
| testcase_20 | AC | 273 ms
40,420 KB |
| testcase_21 | AC | 302 ms
40,324 KB |
| testcase_22 | AC | 307 ms
40,392 KB |
| testcase_23 | AC | 305 ms
40,408 KB |
| testcase_24 | AC | 284 ms
40,416 KB |
| testcase_25 | AC | 271 ms
40,256 KB |
| testcase_26 | AC | 277 ms
40,484 KB |
| testcase_27 | AC | 280 ms
40,384 KB |
| testcase_28 | AC | 271 ms
40,432 KB |
| testcase_29 | AC | 278 ms
40,416 KB |
| testcase_30 | AC | 269 ms
40,368 KB |
| testcase_31 | AC | 265 ms
40,500 KB |
| testcase_32 | AC | 266 ms
40,476 KB |
| testcase_33 | AC | 262 ms
40,424 KB |
ソースコード
#line 2 "/home/nok0/documents/programming/library/template/header.hpp"
#include <bits/stdc++.h>
#line 3 "/home/nok0/documents/programming/library/graph/graph.hpp"
#pragma region graph
template <class cost_type = long long>
class graph {
public:
struct edge {
public:
int from, to;
cost_type cost;
int id;
edge() = default;
edge(int from_, int to_, cost_type cost_ = 1, int id_ = -1) : from(from_), to(to_), cost(cost_), id(id_) {}
bool operator<(const edge &a) const { return cost < a.cost; }
bool operator>(const edge &a) const { return cost > a.cost; }
friend std::ostream &operator<<(std::ostream &s, const edge &a) {
s << '(' << a.from << " -> " << a.to << "), cost: " << a.cost << ", id: " << a.id;
return s;
}
};
private:
std::vector<std::vector<edge>> edges;
int next_edge_id = 0;
public:
inline const std::vector<edge> &operator[](int k) const { return edges[k]; }
inline std::vector<edge> &operator[](int k) { return edges[k]; }
int size() const { return int(edges.size()); }
void resize(const int n) { edges.resize(n); }
int edge_count() const { return next_edge_id; }
friend std::ostream &operator<<(std::ostream &s, const graph<cost_type> &g) {
for(const auto &adj : g.edges)
for(const auto &ed : adj) s << ed << '\n';
return s;
}
graph() = default;
graph(int n) : edges(n) {}
graph(int n, int e, bool weight = 0, bool directed = 0, int idx = 1) : edges(n) { input(e, weight, directed, idx); }
const cost_type INF = std::numeric_limits<cost_type>::max() / 3;
void input(int e = -1, bool weight = false, bool directed = false, int idx = 1) {
if(e == -1) e = size() - 1;
while(e--) {
int u, v;
std::cin >> u >> v;
cost_type cost = 1;
if(weight) std::cin >> cost;
add_edge(u, v, cost, directed, idx);
}
}
inline int add_edge(int u, int v, cost_type cost = 1, bool directed = false, int idx = 0) {
u -= idx, v -= idx;
edges[u].emplace_back(u, v, cost, next_edge_id);
if(!directed && u != v) edges[v].emplace_back(v, u, cost, next_edge_id);
return next_edge_id++;
}
// Ο(V+E)
std::vector<cost_type> bfs(int s) const {
std::vector<cost_type> dist(size(), INF);
std::queue<int> que;
dist[s] = 0;
que.push(s);
while(!que.empty()) {
int v = que.front();
que.pop();
for(auto &e : edges[v]) {
if(dist[e.to] != INF) continue;
dist[e.to] = dist[v] + e.cost;
que.push(e.to);
}
}
return dist;
}
// Ο(V+E)
// constraint: cost of each edge is zero or x (>= 0)
std::vector<cost_type> zero_one_bfs(int s) const {
std::vector<cost_type> dist(size(), INF);
std::deque<int> deq;
dist[s] = 0;
deq.push_back(s);
while(!deq.empty()) {
int v = deq.front();
deq.pop_front();
for(auto &e : edges[v]) {
if(dist[e.to] > dist[v] + e.cost) {
dist[e.to] = dist[v] + e.cost;
e.cost ? deq.push_back(e.to) : deq.push_front(e.to);
}
}
}
return dist;
}
// Ο((E+V) lg E)
// unreachable: INF
std::vector<cost_type> dijkstra(int s) const {
std::vector<cost_type> dist(size(), INF);
const auto compare = [](const std::pair<cost_type, int> &a, const std::pair<cost_type, int> &b) {
return a.first > b.first;
};
std::priority_queue<std::pair<cost_type, int>, std::vector<std::pair<cost_type, int>>, decltype(compare)> que{compare};
dist[s] = 0;
que.emplace(0, s);
while(!que.empty()) {
std::pair<cost_type, int> p = que.top();
que.pop();
int v = p.second;
if(dist[v] < p.first) continue;
for(auto &e : edges[v]) {
if(dist[e.to] > dist[v] + e.cost) {
dist[e.to] = dist[v] + e.cost;
que.emplace(dist[e.to], e.to);
}
}
}
return dist;
}
// Ο(VE)
// unreachable: INF
// reachable via negative cycle: -INF
std::vector<cost_type> bellman_ford(int s) const {
int n = size();
std::vector<cost_type> res(n, INF);
res[s] = 0;
for(int loop = 0; loop < n - 1; loop++) {
for(int v = 0; v < n; v++) {
if(res[v] == INF) continue;
for(auto &e : edges[v]) {
res[e.to] = std::min(res[e.to], res[v] + e.cost);
}
}
}
std::queue<int> que;
std::vector<int> chk(n);
for(int v = 0; v < n; v++) {
if(res[v] == INF) continue;
for(auto &e : edges[v]) {
if(res[e.to] > res[v] + e.cost and !chk[e.to]) {
que.push(e.to);
chk[e.to] = 1;
}
}
}
while(!que.empty()) {
int now = que.front();
que.pop();
for(auto &e : edges[now]) {
if(!chk[e.to]) {
chk[e.to] = 1;
que.push(e.to);
}
}
}
for(int i = 0; i < n; i++)
if(chk[i]) res[i] = -INF;
return res;
}
// Ο(V^3)
std::vector<std::vector<cost_type>> warshall_floyd() const {
const int n = size();
std::vector<std::vector<cost_type>> dist(n, std::vector<cost_type>(n, INF));
for(int i = 0; i < n; i++) dist[i][i] = 0;
for(int i = 0; i < n; i++)
for(auto &e : edges[i]) dist[i][e.to] = std::min(dist[i][e.to], e.cost);
for(int k = 0; k < n; k++)
for(int i = 0; i < n; i++) {
if(dist[i][k] == INF) continue;
for(int j = 0; j < n; j++) {
if(dist[k][j] == INF) continue;
dist[i][j] = std::min(dist[i][j], dist[i][k] + dist[k][j]);
}
}
return dist;
}
// Ο(V) (using DFS)
// if a cycle exists, return {}
std::vector<int> topological_sort() const {
std::vector<int> res;
std::vector<int> used(size(), 0);
bool not_DAG = false;
auto dfs = [&](auto self, int k) -> void {
if(not_DAG) return;
if(used[k]) {
if(used[k] == 1) not_DAG = true;
return;
}
used[k] = 1;
for(auto &e : edges[k]) self(self, e.to);
used[k] = 2;
res.push_back(k);
};
for(int i = 0; i < size(); i++) dfs(dfs, i);
if(not_DAG) return std::vector<int>{};
std::reverse(res.begin(), res.end());
return res;
}
bool is_dag() const { return !topological_sort().empty(); }
// Ο(V)
// array of the distance to the most distant vertex
// constraint: the graph is a tree
std::vector<cost_type> height() const {
auto vec1 = bfs(0);
int v1 = -1, v2 = -1;
cost_type dia = -1;
for(int i = 0; i < int(size()); i++)
if(dia < vec1[i]) dia = vec1[i], v1 = i;
vec1 = bfs(v1);
dia = -1;
for(int i = 0; i < int(size()); i++)
if(dia < vec1[i]) dia = vec1[i], v2 = i;
auto vec2 = bfs(v2);
for(int i = 0; i < int(size()); i++) {
if(vec1[i] < vec2[i]) vec1[i] = vec2[i];
}
return vec1;
}
// O(V+E)
// vector<(int)(0 or 1)>
// if it is not bipartite, return {}
std::vector<int> bipartite_grouping() const {
std::vector<int> colors(size(), -1);
auto dfs = [&](auto self, int now, int col) -> bool {
colors[now] = col;
for(auto &e : edges[now]) {
if(col == colors[e.to]) return false;
if(colors[e.to] == -1 and !self(self, e.to, !col)) return false;
}
return true;
};
for(int i = 0; i < int(size()); i++)
if(colors[i] == -1 and !dfs(dfs, i, 0)) return std::vector<int>{};
return colors;
}
bool is_bipartite() const { return !bipartite_grouping().empty(); }
// Ο(V+E)
// (v1, v2, diameter)
std::tuple<int, int, cost_type> diameter() {
std::vector<cost_type> dist = bfs(0);
auto it = std::max_element(dist.begin(), dist.end());
const int v = it - dist.begin();
dist = bfs(v);
it = std::max_element(dist.begin(), dist.end());
return std::make_tuple(v, int(it - dist.begin()), *it);
}
// Ο(V+E)
std::vector<int> subtree_size(const int root) {
const int n = size();
std::vector<int> ret(n, 1);
auto dfs = [&](auto self, int now, int p = -1) -> void {
for(const auto &e : (*this)[now]) {
if(e.to == p) continue;
self(self, e.to, now);
ret[now] += ret[e.to];
}
};
dfs(dfs, root);
return ret;
}
// Ο(ElgE)
cost_type prim() const {
cost_type res = 0;
std::priority_queue<edge, std::vector<edge>, std::greater<edge>> que;
for(auto &e : edges[0]) que.push(e);
std::vector<int> chk(size());
chk[0] = 1;
int cnt = 1;
while(cnt < size()) {
auto e = que.top();
que.pop();
if(chk[e.to]) continue;
cnt++;
res += e.cost;
chk[e.to] = 1;
for(auto &e2 : edges[e.to]) que.push(e2);
}
return res;
}
// Ο(ElgE)
cost_type kruskal() const {
std::vector<std::tuple<int, int, cost_type>> eds;
for(const auto &adj : edges)
for(const auto &ed : adj) eds.emplace_back(ed.from, ed.to, ed.cost);
std::sort(eds.begin(), eds.end(), [](const std::tuple<int, int, cost_type> &a, const std::tuple<int, int, cost_type> &b) {
return std::get<2>(a) < std::get<2>(b);
});
std::vector<int> uf_data(size(), -1);
auto root = [&uf_data](auto self, int x) -> int {
if(uf_data[x] < 0) return x;
return uf_data[x] = self(self, uf_data[x]);
};
auto unite = [&uf_data, &root](int u, int v) -> bool {
u = root(root, u), v = root(root, v);
if(u == v) return false;
if(uf_data[u] > uf_data[v]) std::swap(u, v);
uf_data[u] += uf_data[v];
uf_data[v] = u;
return true;
};
cost_type ret = 0;
for(auto &e : eds)
if(unite(std::get<0>(e), std::get<1>(e))) ret += std::get<2>(e);
return ret;
}
// O(V)
std::vector<int> centroid() const {
std::vector<int> centroid, sz(size());
auto dfs = [&](auto self, int now, int per) -> void {
sz[now] = 1;
bool is_centroid = true;
for(auto &e : edges[now]) {
if(e.to != per) {
self(self, e.to, now);
sz[now] += sz[e.to];
if(sz[e.to] > size() / 2) is_centroid = false;
}
}
if(size() - sz[now] > size() / 2) is_centroid = false;
if(is_centroid) centroid.push_back(now);
};
dfs(dfs, 0, -1);
return centroid;
}
// O(V+E)
// bridge: (s, t) (s < t);
std::pair<std::vector<std::pair<int, int>>, std::vector<int>> bridges_and_articulations() const {
std::vector<int> order(size(), -1), low(size()), articulation;
int order_next = 0;
std::vector<std::pair<int, int>> bridge;
auto dfs = [&](auto self, int now, int par = -1) -> void {
low[now] = order[now] = order_next++;
bool is_articulation = false;
int cnt = 0;
for(auto &ed : edges[now]) {
int &nxt = ed.to;
if(nxt == par) continue;
if(order[nxt] == -1) {
cnt++;
self(self, nxt, now);
if(order[now] < low[nxt]) bridge.push_back(std::minmax(now, nxt));
if(order[now] <= low[nxt]) is_articulation = true;
low[now] = std::min(low[now], low[nxt]);
} else if(order[now] > order[nxt]) {
low[now] = std::min(low[now], order[nxt]);
}
}
if(par == -1 and cnt < 2) is_articulation = false;
if(is_articulation) articulation.push_back(now);
return;
};
for(int i = 0; i < (int)size(); i++)
if(order[i] == -1) dfs(dfs, i);
return std::make_pair(bridge, articulation);
}
// Ο(V+E)
// directed graph from root to leaf
graph root_to_leaf(int root = 0) const {
graph res(size());
std::vector<int> chk(size(), 0);
chk[root] = 1;
auto dfs = [&](auto self, int now) -> void {
for(auto &e : edges[now]) {
if(chk[e.to] == 1) continue;
chk[e.to] = 1;
res.add_edge(now, e.to, e.cost, 1, 0);
self(self, e.to);
}
};
dfs(dfs, root);
return res;
}
// Ο(V+E)
// directed graph from leaf to root
graph leaf_to_root(int root = 0) const {
graph res(size());
std::vector<int> chk(size(), 0);
chk[root] = 1;
auto dfs = [&](auto self, int now) -> void {
for(auto &e : edges[now]) {
if(chk[e.to] == 1) continue;
chk[e.to] = 1;
res.add_edge(e.to, now, e.cost, 1, 0);
self(self, e.to);
}
};
dfs(dfs, root);
return res;
}
// cost_type Chu_Liu_Edmonds(int root = 0) {}
};
#pragma endregion
#line 3 "/home/nok0/documents/programming/library/graph/namori.hpp"
template <class cost_type>
struct namori {
public:
std::vector<std::vector<int>> cycles;
std::vector<int> cycle_number, root;
namori(graph<cost_type> &g) : n(g.size()), g(g) { build(); }
private:
int n;
std::vector<bool> dfs_used, dfs_now;
std::vector<int> dfs_ver;
graph<cost_type> &g;
graph<cost_type> forest;
void build() {
forest.resize(n);
dfs_used.assign(n, false);
dfs_now.assign(n, false);
dfs_ver.clear();
cycle_number.assign(n, -1);
root.assign(n, -1);
for(int i = 0; i < n; i++) {
if(dfs_used[i]) continue;
cycles.emplace_back();
build_dfs(i, -1, cycles.back());
if(cycles.back().empty()) cycles.back().push_back(i);
}
for(int i = 0; i < (int)cycles.size(); i++)
for(const auto &v : cycles[i]) cycle_number[v] = i;
dfs_used.assign(n, false);
for(int i = 0; i < n; i++)
if(cycle_number[i] != -1) tree_dfs(i, i);
}
void build_dfs(int now, int par, std::vector<int> &cycle) {
dfs_used[now] = true;
dfs_now[now] = true;
dfs_ver.push_back(now);
bool multiple_par = false;
for(const auto &e : g[now]) {
if(dfs_now[e.to] and cycle.empty() and (e.to != par or multiple_par)) {
for(const auto &v : dfs_ver) {
if(!cycle.empty() or v == e.to) cycle.push_back(v);
}
}
if(e.to == par) multiple_par = true;
if(dfs_used[e.to]) continue;
build_dfs(e.to, now, cycle);
}
dfs_now[now] = false;
dfs_ver.pop_back();
}
void tree_dfs(int now, int r) {
dfs_used[now] = true;
root[now] = r;
for(const auto &e : g[now]) {
if(dfs_used[e.to] or cycle_number[e.to] != -1) continue;
forest.add_edge(now, e.to, e.cost);
tree_dfs(e.to, r);
}
}
};
#line 1 "/home/nok0/documents/programming/library/atcoder/modint.hpp"
#line 6 "/home/nok0/documents/programming/library/atcoder/modint.hpp"
#include <type_traits>
#ifdef _MSC_VER
#include <intrin.h>
#endif
#line 1 "/home/nok0/documents/programming/library/atcoder/internal_math.hpp"
#line 5 "/home/nok0/documents/programming/library/atcoder/internal_math.hpp"
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace atcoder {
namespace internal {
// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long 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;
unsigned long long im;
// @param m `1 <= m < 2^31`
explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-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 {
// [1] m = 1
// a = b = im = 0, so okay
// [2] m >= 2
// im = ceil(2^64 / m)
// -> im * m = 2^64 + r (0 <= r < m)
// let z = a*b = c*m + d (0 <= c, d < m)
// a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
// c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
// ((ab * im) >> 64) == c or c + 1
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;
}
};
// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
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;
}
// 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;
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 <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<long long, long long> inv_gcd(long long a, long long b) {
a = safe_mod(a, b);
if (a == 0) return {b, 0};
// Contracts:
// [1] s - m0 * a = 0 (mod b)
// [2] t - m1 * a = 0 (mod b)
// [3] s * |m1| + t * |m0| <= b
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
// [3]:
// (s - t * u) * |m1| + t * |m0 - m1 * u|
// <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
// = s * |m1| + t * |m0| <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
// by [3]: |m0| <= b/g
// by g != b: |m0| < b/g
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; (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 <int m> constexpr int primitive_root = primitive_root_constexpr(m);
// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
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;
// y_max < m * (n + 1)
// floor(y_max / m) <= n
n = (unsigned long long)(y_max / m);
b = (unsigned long long)(y_max % m);
std::swap(m, a);
}
return ans;
}
} // namespace internal
} // namespace atcoder
#line 1 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp"
#line 7 "/home/nok0/documents/programming/library/atcoder/internal_type_traits.hpp"
namespace atcoder {
namespace internal {
#ifndef _MSC_VER
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;
#else
template <class T> using is_integral = typename std::is_integral<T>;
template <class T>
using is_signed_int =
typename std::conditional<is_integral<T>::value && std::is_signed<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,
std::true_type,
std::false_type>::type;
template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
std::make_unsigned<T>,
std::common_type<T>>::type;
#endif
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 atcoder
#line 14 "/home/nok0/documents/programming/library/atcoder/modint.hpp"
namespace atcoder {
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 mint raw(int v) {
mint x;
x._v = v;
return x;
}
static_modint() : _v(0) {}
template <class T, internal::is_signed_int_t<T>* = nullptr>
static_modint(T v) {
long long x = (long long)(v % (long long)(umod()));
if (x < 0) x += umod();
_v = (unsigned int)(x);
}
template <class T, internal::is_unsigned_int_t<T>* = 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<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) {
long long x = (long long)(v % (long long)(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(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 <int id> internal::barrett dynamic_modint<id>::bt(998244353);
using modint998244353 = static_modint<998244353>;
using modint1000000007 = 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 atcoder
#line 4 "/home/nok0/documents/programming/library/math/factorial.hpp"
template <class T>
struct factorial {
private:
int _n;
std::vector<T> _fac, _inv, _finv;
void extend(int n) {
n++;
if(n <= _n) return;
_fac.resize(n);
_inv.resize(n);
_finv.resize(n);
for(int i = _n; i < n; i++) {
_fac[i] = _fac[i - 1] * i;
_inv[i] = (-_inv[T::mod() % i]) * (T::mod() / i);
_finv[i] = _finv[i - 1] * _inv[i];
}
_n = n;
}
public:
explicit factorial(int n = 2) {
_n = 2;
_fac = {1, 1};
_inv = {1, 1};
_finv = {1, 1};
extend(n);
}
T fac(int k) {
extend(k);
return _fac[k];
}
T inv(int k) {
extend(k);
return _inv[k];
}
T finv(int k) {
extend(k);
return _finv[k];
}
T binom(int n, int k) {
if(k < 0 or n < k) return 0;
extend(n);
return _fac[n] * _finv[k] * _finv[n - k];
}
T large_binom(long long n, int k) {
if(k < 0 or n < k) return 0;
extend(k);
T ret = _finv[k];
for(int i = n; i > n - k; i--) ret *= i;
return ret;
}
T catalan(int n) {
extend(n * 2);
return binom(n * 2, n) * _inv[n + 1];
}
T perm(int n, int k) {
if(k < 0 or n < k) return 0;
extend(n);
return _fac[n] * _finv[n - k];
}
};
#line 3 "/home/nok0/documents/programming/library/math/modint_iostream.hpp"
#line 5 "/home/nok0/documents/programming/library/math/modint_iostream.hpp"
template<int m>
std::istream &std::operator>>(std::istream &is, atcoder::static_modint<m> &a) {
long long v;
is >> v;
a = v;
return is;
}
template<int m>
std::istream &std::operator>>(std::istream &is, atcoder::dynamic_modint<m> &a) {
long long v;
is >> v;
a = v;
return is;
}
template<int m>
std::ostream &std::operator<<(std::ostream &os, const atcoder::static_modint<m> &a) { return os << a.val(); }
template<int m>
std::ostream &std::operator<<(std::ostream &os, const atcoder::dynamic_modint<m> &a) { return os << a.val(); }
#line 3 "/home/nok0/documents/programming/library/template/def_const.hpp"
const int inf = 1000000000;
const long long INF = 1000000000000000000ll;
#line 4 "/home/nok0/documents/programming/library/template/debug.hpp"
namespace viewer {
void view(const long long &e) {
if(e == INF)
std::cerr << "INF";
else if(e == -INF)
std::cerr << "-INF";
else
std::cerr << e;
}
void view(const int &e) {
if(e == inf)
std::cerr << "inf";
else if(e == -inf)
std::cerr << "-inf";
else
std::cerr << e;
}
template <typename T>
void view(const T &e) {
std::cerr << e;
}
template <typename T, typename U>
void view(const std::pair<T, U> &p) {
std::cerr << "(";
view(p.first);
std::cerr << ", ";
view(p.second);
std::cerr << ")";
}
template <class T0, class T1, class T2>
void view(const std::tuple<T0, T1, T2> &p) {
std::cerr << "(";
view(std::get<0>(p));
std::cerr << ", ";
view(std::get<1>(p));
std::cerr << ", ";
view(std::get<2>(p));
std::cerr << ")";
}
template <class T0, class T1, class T2, class T3>
void view(const std::tuple<T0, T1, T2, T3> &p) {
std::cerr << "(";
view(std::get<0>(p));
std::cerr << ", ";
view(std::get<1>(p));
std::cerr << ", ";
view(std::get<2>(p));
std::cerr << ", ";
view(std::get<3>(p));
std::cerr << ")";
}
template <typename T>
void view(const std::set<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::unordered_set<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::multiset<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::unordered_multiset<T> &s) {
if(s.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(auto &t : s) {
view(t);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::vector<T> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(const auto &e : v) {
view(e);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T, std::size_t ary_size>
void view(const std::array<T, ary_size> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << "{ ";
for(const auto &e : v) {
view(e);
std::cerr << ", ";
}
std::cerr << "\b\b }";
}
template <typename T>
void view(const std::vector<std::vector<T>> &vv) {
std::cerr << "{\n";
for(const auto &v : vv) {
std::cerr << "\t";
view(v);
std::cerr << '\n';
}
std::cerr << "}";
}
template <typename T, typename U>
void view(const std::vector<std::pair<T, U>> &v) {
std::cerr << "{\n";
for(const auto &c : v) {
std::cerr << "\t(";
view(c.first);
std::cerr << ", ";
view(c.second);
std::cerr << ")\n";
}
std::cerr << "}";
}
template <class T0, class T1, class T2>
void view(const std::vector<std::tuple<T0, T1, T2>> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << '{';
for(const auto &t : v) {
std::cerr << "\n\t";
view(t);
std::cerr << ",";
}
std::cerr << "\n}";
}
template <class T0, class T1, class T2, class T3>
void view(const std::vector<std::tuple<T0, T1, T2, T3>> &v) {
if(v.empty()) {
std::cerr << "{ }";
return;
}
std::cerr << '{';
for(const auto &t : v) {
std::cerr << "\n\t";
view(t);
std::cerr << ",";
}
std::cerr << "\n}";
}
template <typename T, typename U>
void view(const std::map<T, U> &m) {
std::cerr << "{\n";
for(const auto &t : m) {
std::cerr << "\t[";
view(t.first);
std::cerr << "] : ";
view(t.second);
std::cerr << '\n';
}
std::cerr << "}";
}
template <typename T, typename U>
void view(const std::unordered_map<T, U> &m) {
std::cerr << "{\n";
for(const auto &t : m) {
std::cerr << "\t[";
view(t.first);
std::cerr << "] : ";
view(t.second);
std::cerr << '\n';
}
std::cerr << "}";
}
} // namespace viewer
// when compiling : g++ foo.cpp -DLOCAL
#ifdef LOCAL
void debug_out() {}
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
viewer::view(H);
std::cerr << ", ";
debug_out(T...);
}
#define debug(...) \
do { \
std::cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \
debug_out(__VA_ARGS__); \
std::cerr << "\b\b]\n"; \
} while(0)
#define dump(x) \
do { \
std::cerr << __LINE__ << " " << #x << " : "; \
viewer::view(x); \
std::cerr << '\n'; \
} while(0)
#else
#define debug(...) (void(0))
#define dump(x) (void(0))
#endif
#line 3 "/home/nok0/documents/programming/library/template/def_name.hpp"
#define pb push_back
#define eb emplace_back
#define fi first
#define se second
#define SZ(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define popcnt(x) __builtin_popcountll(x)
template <class T = int>
using V = std::vector<T>;
template <class T = int>
using VV = std::vector<std::vector<T>>;
template <class T>
using pqup = std::priority_queue<T, std::vector<T>, std::greater<T>>;
using ll = long long;
using ld = long double;
using int128 = __int128_t;
using pii = std::pair<int, int>;
using pll = std::pair<long long, long long>;
#line 3 "/home/nok0/documents/programming/library/template/fast_io.hpp"
struct fast_io {
fast_io() {
std::ios::sync_with_stdio(false);
std::cin.tie(nullptr);
std::cout << std::fixed << std::setprecision(15);
}
} fast_io_;
#line 3 "/home/nok0/documents/programming/library/template/input.hpp"
template <class T, class U>
std::istream &operator>>(std::istream &is, std::pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <class T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
for(T &i : v) is >> i;
return is;
}
std::istream &operator>>(std::istream &is, __int128_t &a) {
std::string s;
is >> s;
__int128_t ret = 0;
for(int i = 0; i < (int)s.length(); i++)
if('0' <= s[i] and s[i] <= '9')
ret = 10 * ret + s[i] - '0';
a = ret * (s[0] == '-' ? -1 : 1);
return is;
}
namespace scanner {
void scan(int &a) { std::cin >> a; }
void scan(long long &a) { std::cin >> a; }
void scan(std::string &a) { std::cin >> a; }
void scan(char &a) { std::cin >> a; }
void scan(char a[]) { std::ignore = std::scanf("%s", a); }
void scan(double &a) { std::cin >> a; }
void scan(long double &a) { std::cin >> a; }
template <class T, class U>
void scan(std::pair<T, U> &p) { std::cin >> p; }
template <class T>
void scan(std::vector<T> &a) { std::cin >> a; }
void INPUT() {}
template <class Head, class... Tail>
void INPUT(Head &head, Tail &...tail) {
scan(head);
INPUT(tail...);
}
} // namespace scanner
#define VEC(type, name, size) \
std::vector<type> name(size); \
scanner::INPUT(name)
#define VVEC(type, name, h, w) \
std::vector<std::vector<type>> name(h, std::vector<type>(w)); \
scanner::INPUT(name)
#define INT(...) \
int __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define LL(...) \
long long __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define STR(...) \
std::string __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define DOUBLE(...) \
double __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#define LD(...) \
long double __VA_ARGS__; \
scanner::INPUT(__VA_ARGS__)
#line 3 "/home/nok0/documents/programming/library/template/math.hpp"
template <class T, class U>
inline bool chmin(T &a, const U &b) { return a > b ? a = b, true : false; }
template <class T, class U>
inline bool chmax(T &a, const U &b) { return a < b ? a = b, true : false; }
template <class T>
T divup(T x, T y) { return (x + y - 1) / y; }
template <class T>
T POW(T a, long long n) {
T ret = 1;
while(n) {
if(n & 1) ret *= a;
a *= a;
n >>= 1;
}
return ret;
}
long long POW(long long a, long long n, const int mod) {
long long ret = 1;
a = (a % mod + mod) % mod;
while(n) {
if(n & 1) (ret *= a) %= mod;
(a *= a) %= mod;
n >>= 1;
}
return ret;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f) {
while(abs(ok - ng) > 1) {
T mid = (ok + ng) >> 1;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
template <class T, class F>
T bin_search(T ok, T ng, const F &f, int loop) {
for(int i = 0; i < loop; i++) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
#line 3 "/home/nok0/documents/programming/library/template/output.hpp"
template <class T, class U>
std::ostream &operator<<(std::ostream &os, const std::pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &a) {
for(int i = 0; i < int(a.size()); ++i) {
if(i) os << " ";
os << a[i];
}
return os;
}
std::ostream &operator<<(std::ostream &dest, __int128_t &value) {
std::ostream::sentry s(dest);
if(s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while(tmp != 0);
if(value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if(dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
template <class T>
void print(const T a) { std::cout << a << '\n'; }
template <class Head, class... Tail>
void print(Head H, Tail... T) {
std::cout << H << ' ';
print(T...);
}
template <class T>
void println(const T a) { std::cout << a << '\n'; }
template <class T>
void println(const std::vector<T> &a) {
for(const auto &v : a)
std::cout << v << '\n';
}
template <class Head, class... Tail>
void println(Head H, Tail... T) {
std::cout << H << '\n';
println(T...);
}
void Yes(const bool b = true) { std::cout << (b ? "Yes\n" : "No\n"); }
void No() { std::cout << "No\n"; }
void YES(const bool b = true) { std::cout << (b ? "YES\n" : "NO\n"); }
void NO() { std::cout << "NO\n"; }
#line 2 "/home/nok0/documents/programming/library/template/rep.hpp"
#define foa(v, a) for (auto &v : a)
#define repname(a, b, c, d, e, ...) e
#define rep(...) repname(__VA_ARGS__, rep3, rep2, rep1, rep0)(__VA_ARGS__)
#define rep0(x) for (int rep_counter = 0; rep_counter < (x); ++rep_counter)
#define rep1(i, x) for (int i = 0; i < (x); ++i)
#define rep2(i, l, r) for (int i = (l); i < (r); ++i)
#define rep3(i, l, r, c) for (int i = (l); i < (r); i += (c))
#define repsname(a, b, c, ...) c
#define reps(...) repsname(__VA_ARGS__, reps1, reps0)(__VA_ARGS__)
#define reps0(x) for (int reps_counter = 1; reps_counter <= (x); ++reps_counter)
#define reps1(i, x) for (int i = 1; i <= (x); ++i)
#define rrepname(a, b, c, ...) c
#define rrep(...) rrepname(__VA_ARGS__, rrep1, rrep0)(__VA_ARGS__)
#define rrep0(x) for (int rrep_counter = (x)-1; rrep_counter >= 0; --rrep_counter)
#define rrep1(i, x) for (int i = (x)-1; i >= 0; --i)
#line 3 "/home/nok0/documents/programming/library/template/string_converter.hpp"
struct string_converter {
char start = 0;
char type(const char &c) const { return (islower(c) ? 'a' : isupper(c) ? 'A' :
isdigit(c) ? '0' :
0); }
int convert(const char &c) {
if(!start) start = type(c);
return c - start;
}
int convert(const char &c, const std::string &chars) { return chars.find(c); }
template <typename T>
auto convert(const T &v) {
std::vector<decltype(convert(v[0]))> ret;
ret.reserve(size(v));
for(auto &&e : v) ret.emplace_back(convert(e));
return ret;
}
template <typename T>
auto convert(const T &v, const std::string &chars) {
std::vector<decltype(convert(v[0], chars))> ret;
ret.reserve(size(v));
for(auto &&e : v) ret.emplace_back(convert(e, chars));
return ret;
}
int operator()(const char &v, char s = 0) {
start = s;
return convert(v);
}
int operator()(const char &v, const std::string &chars) { return convert(v, chars); }
template <typename T>
auto operator()(const T &v, char s = 0) {
start = s;
return convert(v);
}
template <typename T>
auto operator()(const T &v, const std::string &chars) { return convert(v, chars); }
} toint;
#line 3 "/home/nok0/documents/programming/library/template/vector.hpp"
template <class T>
int lb(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::lower_bound((a).begin(), (a).end(), (x))); }
template <class T>
int ub(const std::vector<T> &a, const T x) { return std::distance((a).begin(), std::upper_bound((a).begin(), (a).end(), (x))); }
template <class T>
void UNIQUE(std::vector<T> &a) {
std::sort(a.begin(), a.end());
a.erase(std::unique(a.begin(), a.end()), a.end());
}
template <class T>
std::vector<T> press(std::vector<T> &a) {
auto res = a;
UNIQUE(res);
for(auto &v : a)
v = lb(res, v);
return res;
}
#define SORTname(a, b, c, ...) c
#define SORT(...) SORTname(__VA_ARGS__, SORT1, SORT0, ...)(__VA_ARGS__)
#define SORT0(a) std::sort((a).begin(), (a).end())
#define SORT1(a, c) std::sort((a).begin(), (a).end(), [](const auto x, const auto y) { return x c y; })
template <class T>
void ADD(std::vector<T> &a, const T x = 1) {
for(auto &v : a) v += x;
}
template <class T>
void SUB(std::vector<T> &a, const T x = 1) {
for(auto &v : a) v -= x;
}
template <class T>
struct cum_vector {
public:
cum_vector() = default;
template <class U>
cum_vector(const std::vector<U> &vec) : cum((int)vec.size() + 1) {
for(int i = 0; i < (int)vec.size(); i++)
cum[i + 1] = cum[i] + vec[i];
}
T prod(int l, int r) {
return cum[r] - cum[l];
}
private:
std::vector<T> cum;
};
std::vector<std::pair<char, int>> rle(const std::string &s) {
const int n = s.size();
std::vector<std::pair<char, int>> ret;
ret.reserve(n);
for(int l = 0; l < n;) {
int r = l + 1;
for(; r < n and s[l] == s[r]; r++) {}
ret.emplace_back(s[l], r - l);
l = r;
}
return ret;
}
template <class T>
std::vector<std::pair<T, int>> rle(const std::vector<T> &v) {
const int n = v.size();
std::vector<std::pair<T, int>> ret;
ret.reserve(n);
for(int l = 0; l < n;) {
int r = l + 1;
for(; r < n and v[l] == v[r]; r++) {}
ret.emplace_back(v[l], r - l);
l = r;
}
return ret;
}
std::vector<int> iota(int n) {
std::vector<int> p(n);
std::iota(p.begin(), p.end(), 0);
return p;
}
#line 12 "/home/nok0/documents/programming/library/template/all"
using namespace std;
#line 5 "g.cpp"
using mint = atcoder::modint998244353;
void main_();
int main() {
int t = 1;
while(t--) main_();
}
void main_() {
INT(n, k);
graph g(n, n);
namori nm(g);
auto cy = nm.cycles[0];
int clen = SZ(cy);
//長さ 3 のサイクルを
mint res = mint(k - 1).pow(n - clen);
vector dp(clen, vector(2, mint(0)));
dp[0][0] = 1;
rep(i, 1, clen) {
dp[i][1] = dp[i - 1][0] * (k - 1) + dp[i - 1][1] * (k - 2);
dp[i][0] = dp[i - 1][1];
}
debug(dp);
mint tmp = dp.back()[1] * k;
print(res * tmp);
}