結果
| 問題 | No.1483 Many Graph in Namori |
| ユーザー |
 maspy
|
| 提出日時 | 2023-11-11 05:40:39 |
| 言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 1,289 ms / 2,000 ms |
| コード長 | 34,431 bytes |
| コンパイル時間 | 7,425 ms |
| コンパイル使用メモリ | 344,440 KB |
| 実行使用メモリ | 66,324 KB |
| 最終ジャッジ日時 | 2024-09-26 02:35:38 |
| 合計ジャッジ時間 | 42,692 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge5 |
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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
5,248 KB |
| testcase_01 | AC | 2 ms
5,248 KB |
| testcase_02 | AC | 2 ms
5,376 KB |
| testcase_03 | AC | 2 ms
5,376 KB |
| testcase_04 | AC | 2 ms
5,376 KB |
| testcase_05 | AC | 1 ms
5,376 KB |
| testcase_06 | AC | 2 ms
5,376 KB |
| testcase_07 | AC | 2 ms
5,376 KB |
| testcase_08 | AC | 2 ms
5,376 KB |
| testcase_09 | AC | 2 ms
5,376 KB |
| testcase_10 | AC | 667 ms
16,848 KB |
| testcase_11 | AC | 380 ms
11,088 KB |
| testcase_12 | AC | 506 ms
14,716 KB |
| testcase_13 | AC | 431 ms
12,372 KB |
| testcase_14 | AC | 517 ms
15,004 KB |
| testcase_15 | AC | 816 ms
20,048 KB |
| testcase_16 | AC | 371 ms
11,088 KB |
| testcase_17 | AC | 161 ms
7,076 KB |
| testcase_18 | AC | 562 ms
16,132 KB |
| testcase_19 | AC | 550 ms
15,596 KB |
| testcase_20 | AC | 380 ms
11,216 KB |
| testcase_21 | AC | 186 ms
7,516 KB |
| testcase_22 | AC | 578 ms
16,216 KB |
| testcase_23 | AC | 630 ms
16,212 KB |
| testcase_24 | AC | 371 ms
10,960 KB |
| testcase_25 | AC | 395 ms
11,600 KB |
| testcase_26 | AC | 888 ms
20,692 KB |
| testcase_27 | AC | 933 ms
23,352 KB |
| testcase_28 | AC | 205 ms
8,176 KB |
| testcase_29 | AC | 422 ms
12,368 KB |
| testcase_30 | AC | 901 ms
23,824 KB |
| testcase_31 | AC | 908 ms
23,824 KB |
| testcase_32 | AC | 912 ms
23,956 KB |
| testcase_33 | AC | 915 ms
23,856 KB |
| testcase_34 | AC | 923 ms
23,740 KB |
| testcase_35 | AC | 513 ms
28,524 KB |
| testcase_36 | AC | 593 ms
32,360 KB |
| testcase_37 | AC | 995 ms
52,128 KB |
| testcase_38 | AC | 227 ms
14,496 KB |
| testcase_39 | AC | 1,289 ms
66,324 KB |
| testcase_40 | AC | 378 ms
11,600 KB |
| testcase_41 | AC | 818 ms
21,328 KB |
| testcase_42 | AC | 623 ms
16,848 KB |
| testcase_43 | AC | 766 ms
20,300 KB |
| testcase_44 | AC | 852 ms
23,640 KB |
| testcase_45 | AC | 65 ms
5,760 KB |
| testcase_46 | AC | 402 ms
18,048 KB |
| testcase_47 | AC | 992 ms
38,516 KB |
| testcase_48 | AC | 1,053 ms
41,160 KB |
| testcase_49 | AC | 1,082 ms
42,360 KB |
| testcase_50 | AC | 855 ms
23,788 KB |
| testcase_51 | AC | 860 ms
23,824 KB |
| testcase_52 | AC | 862 ms
23,940 KB |
| testcase_53 | AC | 863 ms
23,932 KB |
| testcase_54 | AC | 865 ms
23,848 KB |
| testcase_55 | AC | 871 ms
24,000 KB |
| testcase_56 | AC | 1,160 ms
56,136 KB |
| testcase_57 | AC | 1,027 ms
42,228 KB |
| testcase_58 | AC | 855 ms
35,624 KB |
ソースコード
#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using u32 = unsigned int;
using u64 = unsigned long long;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;
template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'000'000'000;
template <>
constexpr ll infty<ll> = ll(infty<int>) * infty<int> * 2;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * infty<ll>;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;
using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;
#define vv(type, name, h, ...) \
vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) \
vector<vector<vector<type>>> name( \
h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
vector<vector<vector<vector<type>>>> name( \
a, vector<vector<vector<type>>>( \
b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))
// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)
#define FOR_subset(t, s) \
for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if
#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second
#define stoi stoll
int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
T floor(T a, T b) {
return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
T q = floor(x, y);
return {q, x - q * y};
}
template <typename T, typename U>
T SUM(const vector<U> &A) {
T sm = 0;
for (auto &&a: A) sm += a;
return sm;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) \
sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()
template <typename T>
T POP(deque<T> &que) {
T a = que.front();
que.pop_front();
return a;
}
template <typename T>
T POP(pq<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(pqg<T> &que) {
T a = que.top();
que.pop();
return a;
}
template <typename T>
T POP(vc<T> &que) {
T a = que.back();
que.pop_back();
return a;
}
template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
if (check_ok) assert(check(ok));
while (abs(ok - ng) > 1) {
auto x = (ng + ok) / 2;
(check(x) ? ok : ng) = x;
}
return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
FOR(iter) {
double x = (ok + ng) / 2;
(check(x) ? ok : ng) = x;
}
return (ok + ng) / 2;
}
template <class T, class S>
inline bool chmax(T &a, const S &b) {
return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
return (a > b ? a = b, 1 : 0);
}
// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
vc<int> A(S.size());
FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
return A;
}
template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
int N = A.size();
vector<T> B(N + 1);
FOR(i, N) { B[i + 1] = B[i] + A[i]; }
if (off == 0) B.erase(B.begin());
return B;
}
// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
vector<int> ids(len(A));
iota(all(ids), 0);
sort(all(ids),
[&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
return ids;
}
// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
vc<T> B(len(I));
FOR(i, len(I)) B[i] = A[I[i]];
return B;
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>
// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;
struct Pre {
char num[10000][4];
constexpr Pre() : num() {
for (int i = 0; i < 10000; i++) {
int n = i;
for (int j = 3; j >= 0; j--) {
num[i][j] = n % 10 | '0';
n /= 10;
}
}
}
} constexpr pre;
inline void load() {
memcpy(ibuf, ibuf + pil, pir - pil);
pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
pil = 0;
if (pir < SZ) ibuf[pir++] = '\n';
}
inline void flush() {
fwrite(obuf, 1, por, stdout);
por = 0;
}
void rd(char &c) {
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
}
void rd(string &x) {
x.clear();
char c;
do {
if (pil + 1 > pir) load();
c = ibuf[pil++];
} while (isspace(c));
do {
x += c;
if (pil == pir) load();
c = ibuf[pil++];
} while (!isspace(c));
}
template <typename T>
void rd_real(T &x) {
string s;
rd(s);
x = stod(s);
}
template <typename T>
void rd_integer(T &x) {
if (pil + 100 > pir) load();
char c;
do
c = ibuf[pil++];
while (c < '-');
bool minus = 0;
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (c == '-') { minus = 1, c = ibuf[pil++]; }
}
x = 0;
while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
if (minus) x = -x;
}
}
void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }
template <class T, class U>
void rd(pair<T, U> &p) {
return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
if constexpr (N < std::tuple_size<T>::value) {
auto &x = std::get<N>(t);
rd(x);
rd_tuple<N + 1>(t);
}
}
template <class... T>
void rd(tuple<T...> &tpl) {
rd_tuple(tpl);
}
template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
for (auto &d: x) rd(d);
}
void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
rd(h), read(t...);
}
void wt(const char c) {
if (por == SZ) flush();
obuf[por++] = c;
}
void wt(const string s) {
for (char c: s) wt(c);
}
void wt(const char *s) {
size_t len = strlen(s);
for (size_t i = 0; i < len; i++) wt(s[i]);
}
template <typename T>
void wt_integer(T x) {
if (por > SZ - 100) flush();
if (x < 0) { obuf[por++] = '-', x = -x; }
int outi;
for (outi = 96; x >= 10000; outi -= 4) {
memcpy(out + outi, pre.num[x % 10000], 4);
x /= 10000;
}
if (x >= 1000) {
memcpy(obuf + por, pre.num[x], 4);
por += 4;
} else if (x >= 100) {
memcpy(obuf + por, pre.num[x] + 1, 3);
por += 3;
} else if (x >= 10) {
int q = (x * 103) >> 10;
obuf[por] = q | '0';
obuf[por + 1] = (x - q * 10) | '0';
por += 2;
} else
obuf[por++] = x | '0';
memcpy(obuf + por, out + outi + 4, 96 - outi);
por += 96 - outi;
}
template <typename T>
void wt_real(T x) {
ostringstream oss;
oss << fixed << setprecision(15) << double(x);
string s = oss.str();
wt(s);
}
void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }
template <class T, class U>
void wt(const pair<T, U> val) {
wt(val.first);
wt(' ');
wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
if constexpr (N < std::tuple_size<T>::value) {
if constexpr (N > 0) { wt(' '); }
const auto x = std::get<N>(t);
wt(x);
wt_tuple<N + 1>(t);
}
}
template <class... T>
void wt(tuple<T...> tpl) {
wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
template <class T>
void wt(const vector<T> val) {
auto n = val.size();
for (size_t i = 0; i < n; i++) {
if (i) wt(' ');
wt(val[i]);
}
}
void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
wt(head);
if (sizeof...(Tail)) wt(' ');
print(forward<Tail>(tail)...);
}
// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;
#define INT(...) \
int __VA_ARGS__; \
read(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
read(__VA_ARGS__)
#define U32(...) \
u32 __VA_ARGS__; \
read(__VA_ARGS__)
#define U64(...) \
u64 __VA_ARGS__; \
read(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
read(__VA_ARGS__)
#define CHAR(...) \
char __VA_ARGS__; \
read(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
read(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
read(name)
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
read(name)
void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 3 "main.cpp"
#line 2 "/home/maspy/compro/library/mod/modint_common.hpp"
struct has_mod_impl {
template <class T>
static auto check(T &&x) -> decltype(x.get_mod(), std::true_type{});
template <class T>
static auto check(...) -> std::false_type;
};
template <class T>
class has_mod : public decltype(has_mod_impl::check<T>(std::declval<T>())) {};
template <typename mint>
mint inv(int n) {
static const int mod = mint::get_mod();
static vector<mint> dat = {0, 1};
assert(0 <= n);
if (n >= mod) n %= mod;
while (len(dat) <= n) {
int k = len(dat);
int q = (mod + k - 1) / k;
dat.eb(dat[k * q - mod] * mint::raw(q));
}
return dat[n];
}
template <typename mint>
mint fact(int n) {
static const int mod = mint::get_mod();
assert(0 <= n && n < mod);
static vector<mint> dat = {1, 1};
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * mint::raw(len(dat)));
return dat[n];
}
template <typename mint>
mint fact_inv(int n) {
static vector<mint> dat = {1, 1};
if (n < 0) return mint(0);
while (len(dat) <= n) dat.eb(dat[len(dat) - 1] * inv<mint>(len(dat)));
return dat[n];
}
template <class mint, class... Ts>
mint fact_invs(Ts... xs) {
return (mint(1) * ... * fact_inv<mint>(xs));
}
template <typename mint, class Head, class... Tail>
mint multinomial(Head &&head, Tail &&... tail) {
return fact<mint>(head) * fact_invs<mint>(std::forward<Tail>(tail)...);
}
template <typename mint>
mint C_dense(int n, int k) {
static vvc<mint> C;
static int H = 0, W = 0;
auto calc = [&](int i, int j) -> mint {
if (i == 0) return (j == 0 ? mint(1) : mint(0));
return C[i - 1][j] + (j ? C[i - 1][j - 1] : 0);
};
if (W <= k) {
FOR(i, H) {
C[i].resize(k + 1);
FOR(j, W, k + 1) { C[i][j] = calc(i, j); }
}
W = k + 1;
}
if (H <= n) {
C.resize(n + 1);
FOR(i, H, n + 1) {
C[i].resize(W);
FOR(j, W) { C[i][j] = calc(i, j); }
}
H = n + 1;
}
return C[n][k];
}
template <typename mint, bool large = false, bool dense = false>
mint C(ll n, ll k) {
assert(n >= 0);
if (k < 0 || n < k) return 0;
if constexpr (dense) return C_dense<mint>(n, k);
if constexpr (!large) return multinomial<mint>(n, k, n - k);
k = min(k, n - k);
mint x(1);
FOR(i, k) x *= mint(n - i);
return x * fact_inv<mint>(k);
}
template <typename mint, bool large = false>
mint C_inv(ll n, ll k) {
assert(n >= 0);
assert(0 <= k && k <= n);
if (!large) return fact_inv<mint>(n) * fact<mint>(k) * fact<mint>(n - k);
return mint(1) / C<mint, 1>(n, k);
}
// [x^d](1-x)^{-n}
template <typename mint, bool large = false, bool dense = false>
mint C_negative(ll n, ll d) {
assert(n >= 0);
if (d < 0) return mint(0);
if (n == 0) { return (d == 0 ? mint(1) : mint(0)); }
return C<mint, large, dense>(n + d - 1, d);
}
#line 3 "/home/maspy/compro/library/mod/modint.hpp"
template <int mod>
struct modint {
static constexpr u32 umod = u32(mod);
static_assert(umod < u32(1) << 31);
u32 val;
static modint raw(u32 v) {
modint x;
x.val = v;
return x;
}
constexpr modint() : val(0) {}
constexpr modint(u32 x) : val(x % umod) {}
constexpr modint(u64 x) : val(x % umod) {}
constexpr modint(u128 x) : val(x % umod) {}
constexpr modint(int x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(ll x) : val((x %= mod) < 0 ? x + mod : x){};
constexpr modint(i128 x) : val((x %= mod) < 0 ? x + mod : x){};
bool operator<(const modint &other) const { return val < other.val; }
modint &operator+=(const modint &p) {
if ((val += p.val) >= umod) val -= umod;
return *this;
}
modint &operator-=(const modint &p) {
if ((val += umod - p.val) >= umod) val -= umod;
return *this;
}
modint &operator*=(const modint &p) {
val = u64(val) * p.val % umod;
return *this;
}
modint &operator/=(const modint &p) {
*this *= p.inverse();
return *this;
}
modint operator-() const { return modint::raw(val ? mod - val : u32(0)); }
modint operator+(const modint &p) const { return modint(*this) += p; }
modint operator-(const modint &p) const { return modint(*this) -= p; }
modint operator*(const modint &p) const { return modint(*this) *= p; }
modint operator/(const modint &p) const { return modint(*this) /= p; }
bool operator==(const modint &p) const { return val == p.val; }
bool operator!=(const modint &p) const { return val != p.val; }
modint inverse() const {
int a = val, b = mod, u = 1, v = 0, t;
while (b > 0) {
t = a / b;
swap(a -= t * b, b), swap(u -= t * v, v);
}
return modint(u);
}
modint pow(ll n) const {
assert(n >= 0);
modint ret(1), mul(val);
while (n > 0) {
if (n & 1) ret *= mul;
mul *= mul;
n >>= 1;
}
return ret;
}
static constexpr int get_mod() { return mod; }
// (n, r), r は 1 の 2^n 乗根
static constexpr pair<int, int> ntt_info() {
if (mod == 167772161) return {25, 17};
if (mod == 469762049) return {26, 30};
if (mod == 754974721) return {24, 362};
if (mod == 880803841) return {23, 211};
if (mod == 943718401) return {22, 663003469};
if (mod == 998244353) return {23, 31};
if (mod == 1045430273) return {20, 363};
if (mod == 1051721729) return {20, 330};
if (mod == 1053818881) return {20, 2789};
return {-1, -1};
}
static constexpr bool can_ntt() { return ntt_info().fi != -1; }
};
#ifdef FASTIO
template <int mod>
void rd(modint<mod> &x) {
fastio::rd(x.val);
assert(0 <= x.val && x.val < mod);
}
template <int mod>
void wt(modint<mod> x) {
fastio::wt(x.val);
}
#endif
using modint107 = modint<1000000007>;
using modint998 = modint<998244353>;
#line 2 "/home/maspy/compro/library/graph/base.hpp"
template <typename T>
struct Edge {
int frm, to;
T cost;
int id;
};
template <typename T = int, bool directed = false>
struct Graph {
static constexpr bool is_directed = directed;
int N, M;
using cost_type = T;
using edge_type = Edge<T>;
vector<edge_type> edges;
vector<int> indptr;
vector<edge_type> csr_edges;
vc<int> vc_deg, vc_indeg, vc_outdeg;
bool prepared;
class OutgoingEdges {
public:
OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}
const edge_type* begin() const {
if (l == r) { return 0; }
return &G->csr_edges[l];
}
const edge_type* end() const {
if (l == r) { return 0; }
return &G->csr_edges[r];
}
private:
const Graph* G;
int l, r;
};
bool is_prepared() { return prepared; }
Graph() : N(0), M(0), prepared(0) {}
Graph(int N) : N(N), M(0), prepared(0) {}
void build(int n) {
N = n, M = 0;
prepared = 0;
edges.clear();
indptr.clear();
csr_edges.clear();
vc_deg.clear();
vc_indeg.clear();
vc_outdeg.clear();
}
void add(int frm, int to, T cost = 1, int i = -1) {
assert(!prepared);
assert(0 <= frm && 0 <= to && to < N);
if (i == -1) i = M;
auto e = edge_type({frm, to, cost, i});
edges.eb(e);
++M;
}
#ifdef FASTIO
// wt, off
void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }
void read_graph(int M, bool wt = false, int off = 1) {
for (int m = 0; m < M; ++m) {
INT(a, b);
a -= off, b -= off;
if (!wt) {
add(a, b);
} else {
T c;
read(c);
add(a, b, c);
}
}
build();
}
#endif
void build() {
assert(!prepared);
prepared = true;
indptr.assign(N + 1, 0);
for (auto&& e: edges) {
indptr[e.frm + 1]++;
if (!directed) indptr[e.to + 1]++;
}
for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
auto counter = indptr;
csr_edges.resize(indptr.back() + 1);
for (auto&& e: edges) {
csr_edges[counter[e.frm]++] = e;
if (!directed)
csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
}
}
OutgoingEdges operator[](int v) const {
assert(prepared);
return {this, indptr[v], indptr[v + 1]};
}
vc<int> deg_array() {
if (vc_deg.empty()) calc_deg();
return vc_deg;
}
pair<vc<int>, vc<int>> deg_array_inout() {
if (vc_indeg.empty()) calc_deg_inout();
return {vc_indeg, vc_outdeg};
}
int deg(int v) {
if (vc_deg.empty()) calc_deg();
return vc_deg[v];
}
int in_deg(int v) {
if (vc_indeg.empty()) calc_deg_inout();
return vc_indeg[v];
}
int out_deg(int v) {
if (vc_outdeg.empty()) calc_deg_inout();
return vc_outdeg[v];
}
#ifdef FASTIO
void debug() {
print("Graph");
if (!prepared) {
print("frm to cost id");
for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
} else {
print("indptr", indptr);
print("frm to cost id");
FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
}
}
#endif
vc<int> new_idx;
vc<bool> used_e;
// G における頂点 V[i] が、新しいグラフで i になるようにする
// {G, es}
Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
if (len(new_idx) != N) new_idx.assign(N, -1);
if (len(used_e) != M) used_e.assign(M, 0);
int n = len(V);
FOR(i, n) new_idx[V[i]] = i;
Graph<T, directed> G(n);
vc<int> history;
FOR(i, n) {
for (auto&& e: (*this)[V[i]]) {
if (used_e[e.id]) continue;
int a = e.frm, b = e.to;
if (new_idx[a] != -1 && new_idx[b] != -1) {
history.eb(e.id);
used_e[e.id] = 1;
int eid = (keep_eid ? e.id : -1);
G.add(new_idx[a], new_idx[b], e.cost, eid);
}
}
}
FOR(i, n) new_idx[V[i]] = -1;
for (auto&& eid: history) used_e[eid] = 0;
G.build();
return G;
}
private:
void calc_deg() {
assert(vc_deg.empty());
vc_deg.resize(N);
for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
}
void calc_deg_inout() {
assert(vc_indeg.empty());
vc_indeg.resize(N);
vc_outdeg.resize(N);
for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
}
};
#line 2 "/home/maspy/compro/library/graph/tree.hpp"
#line 4 "/home/maspy/compro/library/graph/tree.hpp"
// HLD euler tour をとっていろいろ。
template <typename GT>
struct Tree {
using Graph_type = GT;
GT &G;
using WT = typename GT::cost_type;
int N;
vector<int> LID, RID, head, V, parent, VtoE;
vc<int> depth;
vc<WT> depth_weighted;
Tree(GT &G, int r = 0, bool hld = 1) : G(G) { build(r, hld); }
void build(int r = 0, bool hld = 1) {
if (r == -1) return; // build を遅延したいとき
N = G.N;
LID.assign(N, -1), RID.assign(N, -1), head.assign(N, r);
V.assign(N, -1), parent.assign(N, -1), VtoE.assign(N, -1);
depth.assign(N, -1), depth_weighted.assign(N, 0);
assert(G.is_prepared());
int t1 = 0;
dfs_sz(r, -1, hld);
dfs_hld(r, t1);
}
void dfs_sz(int v, int p, bool hld) {
auto &sz = RID;
parent[v] = p;
depth[v] = (p == -1 ? 0 : depth[p] + 1);
sz[v] = 1;
int l = G.indptr[v], r = G.indptr[v + 1];
auto &csr = G.csr_edges;
// 使う辺があれば先頭にする
for (int i = r - 2; i >= l; --i) {
if (hld && depth[csr[i + 1].to] == -1) swap(csr[i], csr[i + 1]);
}
int hld_sz = 0;
for (int i = l; i < r; ++i) {
auto e = csr[i];
if (depth[e.to] != -1) continue;
depth_weighted[e.to] = depth_weighted[v] + e.cost;
VtoE[e.to] = e.id;
dfs_sz(e.to, v, hld);
sz[v] += sz[e.to];
if (hld && chmax(hld_sz, sz[e.to]) && l < i) { swap(csr[l], csr[i]); }
}
}
void dfs_hld(int v, int ×) {
LID[v] = times++;
RID[v] += LID[v];
V[LID[v]] = v;
bool heavy = true;
for (auto &&e: G[v]) {
if (depth[e.to] <= depth[v]) continue;
head[e.to] = (heavy ? head[v] : e.to);
heavy = false;
dfs_hld(e.to, times);
}
}
vc<int> heavy_path_at(int v) {
vc<int> P = {v};
while (1) {
int a = P.back();
for (auto &&e: G[a]) {
if (e.to != parent[a] && head[e.to] == v) {
P.eb(e.to);
break;
}
}
if (P.back() == a) break;
}
return P;
}
int heavy_child(int v) {
int k = LID[v] + 1;
if (k == N) return -1;
int w = V[k];
return (parent[w] == v ? w : -1);
}
int e_to_v(int eid) {
auto e = G.edges[eid];
return (parent[e.frm] == e.to ? e.frm : e.to);
}
int v_to_e(int v) { return VtoE[v]; }
int ELID(int v) { return 2 * LID[v] - depth[v]; }
int ERID(int v) { return 2 * RID[v] - depth[v] - 1; }
// 目標地点へ進む個数が k
int LA(int v, int k) {
assert(k <= depth[v]);
while (1) {
int u = head[v];
if (LID[v] - k >= LID[u]) return V[LID[v] - k];
k -= LID[v] - LID[u] + 1;
v = parent[u];
}
}
int la(int u, int v) { return LA(u, v); }
int LCA(int u, int v) {
for (;; v = parent[head[v]]) {
if (LID[u] > LID[v]) swap(u, v);
if (head[u] == head[v]) return u;
}
}
// root を根とした場合の lca
int LCA_root(int u, int v, int root) {
return LCA(u, v) ^ LCA(u, root) ^ LCA(v, root);
}
int lca(int u, int v) { return LCA(u, v); }
int lca_root(int u, int v, int root) { return LCA_root(u, v, root); }
int subtree_size(int v, int root = -1) {
if (root == -1) return RID[v] - LID[v];
if (v == root) return N;
int x = jump(v, root, 1);
if (in_subtree(v, x)) return RID[v] - LID[v];
return N - RID[x] + LID[x];
}
int dist(int a, int b) {
int c = LCA(a, b);
return depth[a] + depth[b] - 2 * depth[c];
}
WT dist_weighted(int a, int b) {
int c = LCA(a, b);
return depth_weighted[a] + depth_weighted[b] - WT(2) * depth_weighted[c];
}
// a is in b
bool in_subtree(int a, int b) { return LID[b] <= LID[a] && LID[a] < RID[b]; }
int jump(int a, int b, ll k) {
if (k == 1) {
if (a == b) return -1;
return (in_subtree(b, a) ? LA(b, depth[b] - depth[a] - 1) : parent[a]);
}
int c = LCA(a, b);
int d_ac = depth[a] - depth[c];
int d_bc = depth[b] - depth[c];
if (k > d_ac + d_bc) return -1;
if (k <= d_ac) return LA(a, k);
return LA(b, d_ac + d_bc - k);
}
vc<int> collect_child(int v) {
vc<int> res;
for (auto &&e: G[v])
if (e.to != parent[v]) res.eb(e.to);
return res;
}
vc<pair<int, int>> get_path_decomposition(int u, int v, bool edge) {
// [始点, 終点] の"閉"区間列。
vc<pair<int, int>> up, down;
while (1) {
if (head[u] == head[v]) break;
if (LID[u] < LID[v]) {
down.eb(LID[head[v]], LID[v]);
v = parent[head[v]];
} else {
up.eb(LID[u], LID[head[u]]);
u = parent[head[u]];
}
}
if (LID[u] < LID[v]) down.eb(LID[u] + edge, LID[v]);
elif (LID[v] + edge <= LID[u]) up.eb(LID[u], LID[v] + edge);
reverse(all(down));
up.insert(up.end(), all(down));
return up;
}
vc<int> restore_path(int u, int v) {
vc<int> P;
for (auto &&[a, b]: get_path_decomposition(u, v, 0)) {
if (a <= b) {
FOR(i, a, b + 1) P.eb(V[i]);
} else {
FOR_R(i, b, a + 1) P.eb(V[i]);
}
}
return P;
}
};
#line 2 "/home/maspy/compro/library/ds/unionfind/unionfind.hpp"
struct UnionFind {
int n, n_comp;
vc<int> dat; // par or (-size)
UnionFind(int n = 0) { build(n); }
void build(int m) {
n = m, n_comp = m;
dat.assign(n, -1);
}
void reset() { build(n); }
int operator[](int x) {
while (dat[x] >= 0) {
int pp = dat[dat[x]];
if (pp < 0) { return dat[x]; }
x = dat[x] = pp;
}
return x;
}
ll size(int x) {
x = (*this)[x];
return -dat[x];
}
bool merge(int x, int y) {
x = (*this)[x], y = (*this)[y];
if (x == y) return false;
if (-dat[x] < -dat[y]) swap(x, y);
dat[x] += dat[y], dat[y] = x, n_comp--;
return true;
}
};
#line 4 "/home/maspy/compro/library/graph/unicyclic.hpp"
template <typename GT>
struct UnicyclicGraph {
static_assert(!GT::is_directed);
using T = typename GT::cost_type;
GT& G0;
int N;
int root;
int out_eid;
T out_cost;
vc<int> TO;
vc<int> cycle; // 根に向かうような頂点列
vc<bool> in_cycle; // vertex id -> bool
UnicyclicGraph(GT& G) : G0(G), N(G.N) {
assert(N == G.M);
UnionFind uf(N);
TO.assign(N, -1);
FOR(eid, N) {
auto& e = G.edges[eid];
if (uf.merge(e.frm, e.to)) continue;
out_eid = eid, out_cost = e.cost;
root = e.frm;
TO[root] = e.to;
break;
}
vc<bool> done(N);
vc<int> que = {root};
while (len(que)) {
int v = POP(que);
done[v] = 1;
for (auto&& e: G[v]) {
if (done[e.to] || e.id == out_eid) continue;
TO[e.to] = v;
que.eb(e.to);
}
}
cycle = {TO[root]};
while (cycle.back() != root) cycle.eb(TO[cycle.back()]);
in_cycle.assign(N, 0);
for (auto&& v: cycle) in_cycle[v] = 1;
}
// {G, tree}
pair<Graph<T, 1>, Tree<Graph<T, 1>>> build(bool keep_eid = false) {
Graph<T, 1> G(N);
FOR(eid, N) {
if (eid == out_eid) continue;
auto& e = G0.edges[eid];
int a = e.frm, b = e.to;
if (TO[a] == b) swap(a, b);
assert(TO[b] == a);
int k = (keep_eid ? eid : -1);
G.add(a, b, e.cost, k);
}
G.build();
Tree<decltype(G)> tree(G, root);
return {G, tree};
};
template <typename TREE>
int dist(TREE& tree, int a, int b) {
int btm = TO[root];
int ra = tree.lca(a, btm), rb = tree.lca(b, btm);
int d = abs(tree.depth[ra] - tree.depth[rb]);
d = min<int>(d, len(cycle) - d);
return d + tree.depth[a] + tree.depth[b] - tree.depth[ra] - tree.depth[rb];
}
template <typename TREE>
T dist_weighted(TREE& tree, int a, int b) {
int btm = TO[root];
int ra = tree.lca(a, btm), rb = tree.lca(b, btm);
vc<T>& D = tree.depth_weighted;
T d = abs(D[ra] - D[rb]);
d = min(d, D[btm] + out_cost - d);
return d + D[a] + D[b] - D[ra] - D[rb];
}
};
#line 7 "main.cpp"
using mint = modint998;
void solve() {
INT(N, K);
Graph<int, 0> G0(N);
G0.read_graph(N);
UnicyclicGraph<decltype(G0)> UG(G0);
auto [G, tree] = UG.build();
vc<int> cyc = UG.cycle;
int S = cyc[0], T = cyc.back();
mint RX = mint(K) / mint(1 - K);
mint RY = mint(1) / mint(1 - K);
// debug
// RX = 1, RY = 1;
// RX = 2, RY = 1;
// 根の次数, i, j -> sum of RX^x RY^y x^i y^j の和
// i=j=1 は使わないがまとめて実装
using Data = array<array<array<mint, 2>, 2>, 3>;
auto merge_edge = [&](Data& A, Data& B) -> Data {
// 辺属性のマージ
Data S{};
FOR(dA, 3) FOR(dB, 3) {
int d = min<int>(dA + dB, 2);
FOR(i, 2) FOR(j, 2) {
FOR(s, i + 1) FOR(t, j + 1) {
S[d][i][j] += A[dA][s][t] * B[dB][i - s][j - t] * C<mint>(i, s)
* C<mint>(j, t);
}
}
}
return S;
};
auto add_root = [&](Data& A, int k) -> Data {
Data B{};
FOR(d, 3) {
int a = (d + k <= 1);
int b = (d + k >= 2);
FOR(i, 2) FOR(j, 2) {
FOR(s, i + 1) FOR(t, j + 1) {
B[k][i][j] += RX.pow(a) * RY.pow(b) * C<mint>(i, s) * C<mint>(j, t)
* A[d][s][t] * mint(a).pow(i - s) * mint(b).pow(j - t);
}
}
}
return B;
};
mint ANS = 0;
// dp テーブルには根の寄与を含んでいない状態を入れておく
vc<Data> dp(N);
{
auto dfs = [&](auto& dfs, int v) -> Data {
Data A{};
A[0][0][0] = 1;
for (auto& e: G[v]) {
Data B = dfs(dfs, e.to);
B = add_root(B, 1);
// empty
B[0][0][0] = 1;
A = merge_edge(A, B);
}
dp[v] = A;
// print(v);
// FOR(i, 3) print(A[i]);
return A;
};
dfs(dfs, T);
// とりあえず TS 辺を含まないやつはできている
FOR(v, N) {
Data A = dp[v];
A = add_root(A, 0);
FOR(k, 3) ANS += A[k][0][1] + A[k][1][0];
}
// print(ANS);
}
// サイクル辺を使わずに部分木の状態を保持する計算でやり直し
{
auto dfs = [&](auto& dfs, int v) -> Data {
Data A{};
A[0][0][0] = 1;
for (auto& e: G[v]) {
Data B = dfs(dfs, e.to);
if (UG.in_cycle[e.to]) continue;
B = add_root(B, 1);
// empty
B[0][0][0] = 1;
A = merge_edge(A, B);
}
dp[v] = A;
// print(v);
// FOR(i, 3) print(A[i]);
return A;
};
dfs(dfs, T);
}
// サイクル全体を含む場合を計算する
{
Data A{};
A[0][0][0] = 1;
for (auto& v: cyc) {
Data B = add_root(dp[v], 2);
A = merge_edge(A, B);
}
FOR(k, 3) ANS += A[k][0][1] + A[k][1][0];
}
dp = rearrange(dp, cyc);
int n = len(dp);
using ARR = array<array<mint, 2>, 2>;
auto merge = [&](ARR& A, ARR& B) -> ARR {
ARR S{};
FOR(i, 2) {
FOR(j, 2) {
FOR(s, i + 1) FOR(t, j + 1) {
S[i][j] += A[s][t] * B[i - s][j - t] * C<mint>(i, s) * C<mint>(j, t);
}
}
}
return S;
};
// 両端がつながっていてどこかが切れている場合を計算する
// 辺が 1, 2 個追加される場合の頂点属性
vc<ARR> dp1(n), dp2(n);
FOR(i, n) {
Data A = add_root(dp[i], 1);
FOR(k, 3) FOR(a, 2) FOR(b, 2) dp1[i][a][b] += A[k][a][b];
A = add_root(dp[i], 2);
FOR(k, 3) FOR(a, 2) FOR(b, 2) dp2[i][a][b] += A[k][a][b];
}
ARR unit{};
unit[0][0] = 1;
// あとここだけ. 意外と楽か？
// 2221...1222
/*
FOR(b, n) FOR(a, b) {
ARR x = unit;
FOR(i, a) x = merge(x, dp2[i]);
x = merge(x, dp1[a]);
x = merge(x, dp1[b]);
FOR(i, b + 1, n) x = merge(x, dp2[i]);
ANS += x[0][1] + x[1][0];
}
*/
// i 番目に 1 が来るとき
vc<ARR> DPL(n), DPR(n);
ARR x = unit;
FOR(i, n) {
DPL[i] = merge(x, dp1[i]);
x = merge(x, dp2[i]);
}
x = unit;
FOR_R(i, n) {
DPR[i] = merge(x, dp1[i]);
x = merge(x, dp2[i]);
}
// suffix を累積和にする
FOR_R(i, n - 1) { FOR(a, 2) FOR(b, 2) DPR[i][a][b] += DPR[i + 1][a][b]; }
FOR(i, n - 1) {
ARR x = DPL[i], y = DPR[i + 1];
x = merge(x, y);
ANS += x[0][1] + x[1][0];
}
ANS *= mint(1 - K).pow(N);
print(ANS);
}
signed main() {
int T = 1;
// INT(T);
FOR(T) solve();
return 0;
}