結果
| 問題 | No.2116 Making Forest Hard |
| ユーザー |
 noimi
|
| 提出日時 | 2022-10-14 04:25:41 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 57,503 bytes |
| コンパイル時間 | 6,873 ms |
| コンパイル使用メモリ | 354,888 KB |
| 実行使用メモリ | 640,876 KB |
| 最終ジャッジ日時 | 2024-06-26 12:22:05 |
| 合計ジャッジ時間 | 44,243 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
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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
6,812 KB |
| testcase_01 | WA | - |
| testcase_02 | WA | - |
| testcase_03 | WA | - |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | MLE | - |
| testcase_07 | WA | - |
| testcase_08 | AC | 629 ms
447,708 KB |
| testcase_09 | MLE | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
| testcase_12 | MLE | - |
| testcase_13 | WA | - |
| testcase_14 | WA | - |
| testcase_15 | WA | - |
| testcase_16 | MLE | - |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | AC | 355 ms
260,544 KB |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
| testcase_22 | WA | - |
| testcase_23 | WA | - |
| testcase_24 | WA | - |
| testcase_25 | WA | - |
| testcase_26 | MLE | - |
| testcase_27 | WA | - |
| testcase_28 | WA | - |
| testcase_29 | WA | - |
| testcase_30 | WA | - |
| testcase_31 | WA | - |
| testcase_32 | WA | - |
| testcase_33 | WA | - |
| testcase_34 | WA | - |
| testcase_35 | WA | - |
| testcase_36 | AC | 602 ms
449,184 KB |
| testcase_37 | WA | - |
| testcase_38 | MLE | - |
| testcase_39 | WA | - |
| testcase_40 | WA | - |
| testcase_41 | WA | - |
| testcase_42 | WA | - |
| testcase_43 | WA | - |
| testcase_44 | WA | - |
| testcase_45 | WA | - |
| testcase_46 | WA | - |
| testcase_47 | WA | - |
| testcase_48 | WA | - |
| testcase_49 | AC | 2 ms
6,940 KB |
| testcase_50 | WA | - |
| testcase_51 | WA | - |
| testcase_52 | WA | - |
| testcase_53 | WA | - |
| testcase_54 | WA | - |
ソースコード
#pragma region Macros
#pragma comment(linker, "/stack:400000000")
#if defined(noimi) && defined(_GLIBCXX_DEBUG) && defined(_GLIBCXX_DEBUG_PEDANTIC)
#include <stdc++.h>
#pragma GCC optimize("O3")
#else
#pragma GCC optimize("O2")
// #pragma GCC optimize("unroll-loops")
// #pragma GCC target("popcnt")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,fma,abm,mmx,avx,avx2,tune=native")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,fma,abm,mmx,avx,avx2")
// #pragma GCC target("avx2")
// #include <bits/stdc++.h>
// #include <bits/stdc++.h>
#include <immintrin.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#endif
#include <cstdint>
#include <immintrin.h>
#include <variant>
#ifdef noimi
#define oj_local(a, b) b
#else
#define oj_local(a, b) a
#endif
#define LOCAL if(oj_local(0, 1))
#define OJ if(oj_local(1, 0))
using namespace std;
using ll = long long;
using ull = unsigned long long int;
using i128 = __int128_t;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using ld = long double;
template <typename T> using vc = vector<T>;
template <typename T> using vvc = vector<vc<T>>;
template <typename T> using vvvc = vector<vvc<T>>;
using vi = vc<int>;
using vl = vc<ll>;
using vpi = vc<pii>;
using vpl = vc<pll>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>;
template <typename T> int si(const T &x) { return x.size(); }
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); }
vi iota(int n) {
vi a(n);
return iota(a.begin(), a.end(), 0), a;
}
template <typename T> vi iota(const vector<T> &a, bool greater = false) {
vi res(a.size());
iota(res.begin(), res.end(), 0);
sort(res.begin(), res.end(), [&](int i, int j) {
if(greater) return a[i] > a[j];
return a[i] < a[j];
});
return res;
}
// macros
#define overload5(a, b, c, d, e, name, ...) name
#define overload4(a, b, c, d, name, ...) name
#define endl '\n'
#define REP0(n) for(ll jidlsjf = 0; jidlsjf < n; ++jidlsjf)
#define REP1(i, n) for(ll i = 0; i < (n); ++i)
#define REP2(i, a, b) for(ll i = (a); i < (b); ++i)
#define REP3(i, a, b, c) for(ll i = (a); i < (b); i += (c))
#define rep(...) overload4(__VA_ARGS__, REP3, REP2, REP1, REP0)(__VA_ARGS__)
#define per0(n) for(int jidlsjf = 0; jidlsjf < (n); ++jidlsjf)
#define per1(i, n) for(ll i = (n)-1; i >= 0; --i)
#define per2(i, a, b) for(ll i = (a)-1; i >= b; --i)
#define per3(i, a, b, c) for(ll i = (a)-1; i >= (b); i -= (c))
#define per(...) overload4(__VA_ARGS__, per3, per2, per1, per0)(__VA_ARGS__)
#define fore0(a) rep(a.size())
#define fore1(i, a) for(auto &&i : a)
#define fore2(a, b, v) for(auto &&[a, b] : v)
#define fore3(a, b, c, v) for(auto &&[a, b, c] : v)
#define fore4(a, b, c, d, v) for(auto &&[a, b, c, d] : v)
#define fore(...) overload5(__VA_ARGS__, fore4, fore3, fore2, fore1, fore0)(__VA_ARGS__)
#define fi first
#define se second
#define pb push_back
#define ppb pop_back
#define ppf pop_front
#define eb emplace_back
#define drop(s) cout << #s << endl, exit(0)
#define si(c) (int)(c).size()
#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 rng(v, l, r) v.begin() + (l), v.begin() + (r)
#define all(c) begin(c), end(c)
#define rall(c) rbegin(c), rend(c)
#define SORT(v) sort(all(v))
#define REV(v) reverse(all(v))
#define UNIQUE(x) SORT(x), x.erase(unique(all(x)), x.end())
template <typename T = ll, typename S> T SUM(const S &v) { return accumulate(all(v), T(0)); }
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define overload2(_1, _2, name, ...) name
#define vec(type, name, ...) vector<type> name(__VA_ARGS__)
#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__))))
constexpr pii dx4[4] = {pii{1, 0}, pii{0, 1}, pii{-1, 0}, pii{0, -1}};
constexpr pii dx8[8] = {{1, 0}, {1, 1}, {0, 1}, {-1, 1}, {-1, 0}, {-1, -1}, {0, -1}, {1, -1}};
namespace yesno_impl {
const string YESNO[2] = {"NO", "YES"};
const string YesNo[2] = {"No", "Yes"};
const string yesno[2] = {"no", "yes"};
const string firstsecond[2] = {"second", "first"};
const string FirstSecond[2] = {"Second", "First"};
const string possiblestr[2] = {"impossible", "possible"};
const string Possiblestr[2] = {"Impossible", "Possible"};
void YES(bool t = 1) { cout << YESNO[t] << endl; }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { cout << YesNo[t] << endl; }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { cout << yesno[t] << endl; }
void no(bool t = 1) { yes(!t); }
void first(bool t = 1) { cout << firstsecond[t] << endl; }
void First(bool t = 1) { cout << FirstSecond[t] << endl; }
void possible(bool t = 1) { cout << possiblestr[t] << endl; }
void Possible(bool t = 1) { cout << Possiblestr[t] << endl; }
}; // namespace yesno_impl
using namespace yesno_impl;
#define INT(...) \
int __VA_ARGS__; \
IN(__VA_ARGS__)
#define LL(...) \
ll __VA_ARGS__; \
IN(__VA_ARGS__)
#define STR(...) \
string __VA_ARGS__; \
IN(__VA_ARGS__)
#define CHR(...) \
char __VA_ARGS__; \
IN(__VA_ARGS__)
#define DBL(...) \
double __VA_ARGS__; \
IN(__VA_ARGS__)
#define VEC(type, name, size) \
vector<type> name(size); \
IN(name)
#define VEC2(type, name1, name2, size) \
vector<type> name1(size), name2(size); \
for(int i = 0; i < size; i++) IN(name1[i], name2[i])
#define VEC3(type, name1, name2, name3, size) \
vector<type> name1(size), name2(size), name3(size); \
for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i])
#define VEC4(type, name1, name2, name3, name4, size) \
vector<type> name1(size), name2(size), name3(size), name4(size); \
for(int i = 0; i < size; i++) IN(name1[i], name2[i], name3[i], name4[i]);
#define VV(type, name, h, w) \
vector<vector<type>> name(h, vector<type>(w)); \
IN(name)
int scan() { return getchar(); }
void scan(int &a) { cin >> a; }
void scan(long long &a) { cin >> a; }
void scan(char &a) { cin >> a; }
void scan(double &a) { cin >> a; }
void scan(string &a) { cin >> a; }
template <class T, class S> void scan(pair<T, S> &p) { scan(p.first), scan(p.second); }
template <class T> void scan(vector<T> &);
template <class T> void scan(vector<T> &a) {
for(auto &i : a) scan(i);
}
template <class T> void scan(T &a) { cin >> a; }
void IN() {}
template <class Head, class... Tail> void IN(Head &head, Tail &...tail) {
scan(head);
IN(tail...);
}
template <typename T, typename S> T ceil(T x, S y) {
assert(y);
return (y < 0 ? ceil(-x, -y) : (x > 0 ? (x + y - 1) / y : x / y));
}
template <typename T, typename S> T floor(T x, S y) {
assert(y);
return (y < 0 ? floor(-x, -y) : (x > 0 ? x / y : x / y - (x % y == 0 ? 0 : 1)));
}
template <class T> T POW(T x, int n) {
T res = 1;
for(; n; n >>= 1, x *= x)
if(n & 1) res *= x;
return res;
}
template <class T, class S> T POW(T x, S n, const ll &mod) {
T res = 1;
x %= mod;
for(; n; n >>= 1, x = x * x % mod)
if(n & 1) res = res * x % mod;
return res;
}
vector<pll> factor(ll x) {
vector<pll> ans;
for(ll i = 2; i * i <= x; i++)
if(x % i == 0) {
ans.push_back({i, 1});
while((x /= i) % i == 0) ans.back().second++;
}
if(x != 1) ans.push_back({x, 1});
return ans;
}
template <class T> vector<T> divisor(T x) {
vector<T> ans;
for(T i = 1; i * i <= x; i++)
if(x % i == 0) {
ans.pb(i);
if(i * i != x) ans.pb(x / i);
}
return ans;
}
template <typename T> void zip(vector<T> &x) {
vector<T> y = x;
UNIQUE(y);
for(int i = 0; i < x.size(); ++i) { x[i] = lb(y, x[i]); }
}
template <class S> void fold_in(vector<S> &v) {}
template <typename Head, typename... Tail, class S> void fold_in(vector<S> &v, Head &&a, Tail &&...tail) {
for(auto e : a) v.emplace_back(e);
fold_in(v, tail...);
}
template <class S> void renumber(vector<S> &v) {}
template <typename Head, typename... Tail, class S> void renumber(vector<S> &v, Head &&a, Tail &&...tail) {
for(auto &&e : a) e = lb(v, e);
renumber(v, tail...);
}
template <class S, class... Args> vector<S> zip(vector<S> &head, Args &&...args) {
vector<S> v;
fold_in(v, head, args...);
sort(all(v)), v.erase(unique(all(v)), v.end());
renumber(v, head, args...);
return v;
}
template <typename T> vector<T> RUI(const vector<T> &v) {
vector<T> res(v.size() + 1);
for(int i = 0; i < v.size(); i++) res[i + 1] = res[i] + v[i];
return res;
}
template <typename T> void zeta_subset(vector<T> &f) {
int n = f.size();
for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b] += f[b | i];
}
template <typename T> void zeta_superset(vector<T> &f) {
int n = f.size();
for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b | i] += f[b];
}
template <typename T> void mobius_subset(vector<T> &f) {
int n = f.size();
for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b] -= f[b | i];
}
template <typename T> void mobius_superset(vector<T> &f) {
int n = f.size();
for(int i = 1; i < n; i <<= 1) rep(b, n) if(!(i & b)) f[b | i] -= f[b];
}
// 反時計周りに 90 度回転
template <typename T> void rot(vector<vector<T>> &v) {
if(empty(v)) return;
int n = v.size(), m = v[0].size();
vector res(m, vector<T>(n));
rep(i, n) rep(j, m) res[m - 1 - j][i] = v[i][j];
v.swap(res);
}
// x in [l, r)
template <class T, class S> bool inc(const T &x, const S &l, const S &r) { return l <= x and x < r; }
// 便利関数
constexpr ll ten(int n) { return n == 0 ? 1 : ten(n - 1) * 10; }
constexpr ll tri(ll n) { return n * (n + 1) / 2; }
// l + ... + r
constexpr ll tri(ll l, ll r) { return (l + r) * (r - l + 1) / 2; }
ll max(int x, ll y) { return max((ll)x, y); }
ll max(ll x, int y) { return max(x, (ll)y); }
int min(int x, ll y) { return min((ll)x, y); }
int min(ll x, int y) { return min(x, (ll)y); }
// bit 演算系
ll pow2(int i) { return 1LL << i; }
int topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
int topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
int lowbit(signed a) { return a == 0 ? 32 : __builtin_ctz(a); }
int lowbit(ll a) { return a == 0 ? 64 : __builtin_ctzll(a); }
// int allbit(int n) { return (1 << n) - 1; }
constexpr ll mask(int n) { return (1LL << n) - 1; }
// int popcount(signed t) { return __builtin_popcount(t); }
// int popcount(ll t) { return __builtin_popcountll(t); }
int popcount(uint64_t t) { return __builtin_popcountll(t); }
static inline uint64_t popcount64(uint64_t x) {
uint64_t m1 = 0x5555555555555555ll;
uint64_t m2 = 0x3333333333333333ll;
uint64_t m4 = 0x0F0F0F0F0F0F0F0Fll;
uint64_t h01 = 0x0101010101010101ll;
x -= (x >> 1) & m1;
x = (x & m2) + ((x >> 2) & m2);
x = (x + (x >> 4)) & m4;
return (x * h01) >> 56;
}
bool ispow2(int i) { return i && (i & -i) == i; }
ll rnd(ll l, ll r) { //[l, r)
#ifdef noimi
static mt19937_64 gen;
#else
static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
#endif
return uniform_int_distribution<ll>(l, r - 1)(gen);
}
ll rnd(ll n) { return rnd(0, n); }
template <class t> void random_shuffle(vc<t> &a) { rep(i, si(a)) swap(a[i], a[rnd(0, i + 1)]); }
int in() {
int x;
cin >> x;
return x;
}
ll lin() {
unsigned long long x;
cin >> x;
return x;
}
template <class T, class S> pair<T, S> operator-(const pair<T, S> &x) { return pair<T, S>(-x.first, -x.second); }
template <class T, class S> pair<T, S> operator-(const pair<T, S> &x, const pair<T, S> &y) { return pair<T, S>(x.fi - y.fi, x.se - y.se); }
template <class T, class S> pair<T, S> operator+(const pair<T, S> &x, const pair<T, S> &y) { return pair<T, S>(x.fi + y.fi, x.se + y.se); }
template <class T> pair<T, T> operator&(const pair<T, T> &l, const pair<T, T> &r) { return pair<T, T>(max(l.fi, r.fi), min(l.se, r.se)); }
template <class T, class S> pair<T, S> operator+=(pair<T, S> &l, const pair<T, S> &r) { return l = l + r; }
template <class T, class S> pair<T, S> operator-=(pair<T, S> &l, const pair<T, S> &r) { return l = l - r; }
template <class T> bool intersect(const pair<T, T> &l, const pair<T, T> &r) { return (l.se < r.se ? r.fi < l.se : l.fi < r.se); }
template <typename T> struct edge {
int from, to;
T cost;
int id;
edge(int to, T cost) : from(-1), to(to), cost(cost) {}
edge(int from, int to, T cost) : from(from), to(to), cost(cost) {}
edge(int from, int to, T cost, int id) : from(from), to(to), cost(cost), id(id) {}
constexpr bool operator<(const edge<T> &rhs) const noexcept { return cost < rhs.cost; }
edge &operator=(const int &x) {
to = x;
return *this;
}
operator int() const { return to; }
friend ostream operator<<(ostream &os, edge &e) { return os << e.to; }
};
template <typename T> using Edges = vector<edge<T>>;
using Tree = vector<vector<int>>;
using Graph = vector<vector<int>>;
template <class T> using Wgraph = vector<vector<edge<T>>>;
Graph getG(int n, int m = -1, bool directed = false, int margin = 1) {
Tree res(n);
if(m == -1) m = n - 1;
while(m--) {
int a, b;
cin >> a >> b;
a -= margin, b -= margin;
res[a].emplace_back(b);
if(!directed) res[b].emplace_back(a);
}
return res;
}
Graph getTreeFromPar(int n, int margin = 1) {
Graph res(n);
for(int i = 1; i < n; i++) {
int a;
cin >> a;
res[a - margin].emplace_back(i);
}
return res;
}
template <class T> Wgraph<T> getWg(int n, int m = -1, bool directed = false, int margin = 1) {
Wgraph<T> res(n);
if(m == -1) m = n - 1;
while(m--) {
int a, b;
T c;
scan(a), scan(b), scan(c);
a -= margin, b -= margin;
res[a].emplace_back(b, c);
if(!directed) res[b].emplace_back(a, c);
}
return res;
}
void add(Graph &G, int x, int y) { G[x].eb(y), G[y].eb(x); }
template <class S, class T> void add(Wgraph<S> &G, int x, int y, T c) { G[x].eb(y, c), G[y].eb(x, c); }
#define TEST \
INT(testcases); \
while(testcases--)
i128 abs(const i128 &x) { return x > 0 ? x : -x; }
istream &operator>>(istream &is, i128 &v) {
string s;
is >> s;
v = 0;
for(int i = 0; i < (int)s.size(); i++) {
if(isdigit(s[i])) { v = v * 10 + s[i] - '0'; }
}
if(s[0] == '-') { v *= -1; }
return is;
}
ostream &operator<<(ostream &os, const i128 &v) {
if(v == 0) { return (os << "0"); }
i128 num = v;
if(v < 0) {
os << '-';
num = -num;
}
string s;
for(; num > 0; num /= 10) { s.push_back((char)(num % 10) + '0'); }
reverse(s.begin(), s.end());
return (os << s);
}
namespace aux {
template <typename T, unsigned N, unsigned L> struct tp {
static void output(std::ostream &os, const T &v) {
os << std::get<N>(v) << (&os == &cerr ? ", " : " ");
tp<T, N + 1, L>::output(os, v);
}
};
template <typename T, unsigned N> struct tp<T, N, N> {
static void output(std::ostream &os, const T &v) { os << std::get<N>(v); }
};
} // namespace aux
template <typename... Ts> std::ostream &operator<<(std::ostream &os, const std::tuple<Ts...> &t) {
if(&os == &cerr) { os << '('; }
aux::tp<std::tuple<Ts...>, 0, sizeof...(Ts) - 1>::output(os, t);
if(&os == &cerr) { os << ')'; }
return os;
}
template <class T, class S> ostream &operator<<(ostream &os, const pair<T, S> &p) {
if(&os == &cerr) { return os << "(" << p.first << ", " << p.second << ")"; }
return os << p.first << " " << p.second;
}
template <class Ch, class Tr, class Container> std::basic_ostream<Ch, Tr> &operator<<(std::basic_ostream<Ch, Tr> &os, const Container &x) {
bool f = true;
if(&os == &cerr) os << "[";
for(auto &y : x) {
if(&os == &cerr)
os << (f ? "" : ", ") << y;
else
os << (f ? "" : " ") << y;
f = false;
}
if(&os == &cerr) os << "]";
return os;
}
#ifdef noimi
#undef endl
void debug() { cerr << endl; }
void debug(bool) { cerr << endl; }
template <class Head, class... Tail> void debug(bool is_front, Head head, Tail... tail) {
if(!is_front) cerr << ", ";
cerr << head;
debug(false, tail...);
}
#define dump(args...) \
{ \
vector<string> _debug = _split(#args, ','); \
err(true, begin(_debug), args); \
}
vector<string> _split(const string &s, char c) {
vector<string> v;
stringstream ss(s);
string x;
while(getline(ss, x, c)) {
if(empty(v))
v.eb(x);
else {
bool flag = false;
for(auto [c, d] : {pair('(', ')'), pair('[', ']'), pair('{', '}')}) {
if(count(all(v.back()), c) != count(all(v.back()), d)) flag = true;
}
if(flag)
v.back() += "," + x;
else
v.eb(x);
}
}
return move(v);
}
void err(bool, vector<string>::iterator) { cerr << endl; }
template <typename T, typename... Args> void err(bool is_front, vector<string>::iterator it, T a, Args... args) {
if(!is_front) cerr << ", ";
cerr << it->substr((*it)[0] == ' ', (*it).size()) << " = " << a, err(false, ++it, args...);
}
// #define dump(...) cerr << #__VA_ARGS__ << " : ", debug(true, __VA_ARGS__)
#else
#define dump(...) static_cast<void>(0)
#define dbg(...) static_cast<void>(0)
#endif
void OUT() { cout << endl; }
template <class Head, class... Tail> void OUT(const Head &head, const Tail &...tail) {
cout << head;
if(sizeof...(tail)) cout << ' ';
OUT(tail...);
}
template <typename T> static constexpr T inf = numeric_limits<T>::max() / 2;
template <class T, class S> constexpr pair<T, S> inf<pair<T, S>> = {inf<T>, inf<S>};
template <class F> struct REC {
F f;
REC(F &&f_) : f(std::forward<F>(f_)) {}
template <class... Args> auto operator()(Args &&...args) const { return f(*this, std::forward<Args>(args)...); }
};
template <class S> vector<pair<S, int>> runLength(const vector<S> &v) {
vector<pair<S, int>> res;
for(auto &e : v) {
if(res.empty() or res.back().fi != e)
res.eb(e, 1);
else
res.back().se++;
}
return res;
}
vector<pair<char, int>> runLength(const string &v) {
vector<pair<char, int>> res;
for(auto &e : v) {
if(res.empty() or res.back().fi != e)
res.eb(e, 1);
else
res.back().se++;
}
return res;
}
int toint(const char &c, const char start = 'a') { return c - start; }
int toint(const char &c, const string &chars) { return find(all(chars), c) - begin(chars); }
int alphabets_to_int(const char &c) { return (islower(c) ? c - 'a' : c - 'A' + 26); }
template <typename T> auto toint(const T &v, const char &start = 'a') {
vector<decltype(toint(v[0]))> ret;
ret.reserve(v.size());
for(auto &&e : v) ret.emplace_back(toint(e, start));
return ret;
}
template <typename T> auto toint(const T &v, const string &start) {
vector<decltype(toint(v[0]))> ret;
ret.reserve(v.size());
for(auto &&e : v) ret.emplace_back(toint(e, start));
return ret;
}
// a -> 0, A -> 26
template <typename T> auto alphabets_to_int(const T &s) {
vector<decltype(alphabets_to_int(s[0]))> res;
res.reserve(s.size());
for(auto &&e : s) { res.emplace_back(alphabets_to_int(e)); }
return res;
}
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_double(T ok, T ng, const F &f, int iter = 80) {
while(iter--) {
T mid = (ok + ng) / 2;
(f(mid) ? ok : ng) = mid;
}
return ok;
}
struct Setup_io {
Setup_io() {
ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
cout << fixed << setprecision(11);
}
} setup_io;
#pragma endregion
namespace modular {
constexpr int MOD = 998244353;
const int MAXN = 11000000;
template <int Modulus> class modint;
using mint = modint<MOD>;
using vmint = vector<mint>;
vector<mint> Inv;
mint inv(int x);
template <int Modulus> class modint {
public:
static constexpr int mod() { return Modulus; }
int a;
constexpr modint(const ll x = 0) noexcept : a(((x % Modulus) + Modulus) % Modulus) {}
constexpr int &val() noexcept { return a; }
constexpr const int &val() const noexcept { return a; }
constexpr modint operator-() const noexcept { return modint() - *this; }
constexpr modint operator+() const noexcept { return *this; }
constexpr modint &operator++() noexcept {
if(++a == MOD) a = 0;
return *this;
}
constexpr modint &operator--() noexcept {
if(!a) a = MOD;
a--;
return *this;
}
constexpr modint operator++(int) {
modint res = *this;
++*this;
return res;
}
constexpr modint operator--(int) {
mint res = *this;
--*this;
return res;
}
constexpr modint &operator+=(const modint rhs) noexcept {
a += rhs.a;
if(a >= Modulus) { a -= Modulus; }
return *this;
}
constexpr modint &operator-=(const modint rhs) noexcept {
if(a < rhs.a) { a += Modulus; }
a -= rhs.a;
return *this;
}
constexpr modint &operator*=(const modint rhs) noexcept {
a = (long long)a * rhs.a % Modulus;
return *this;
}
constexpr modint &operator/=(const modint rhs) noexcept {
a = (long long)a * (modular::inv(rhs.a)).a % Modulus;
return *this;
}
constexpr modint pow(long long n) const noexcept {
if(n < 0) {
n %= Modulus - 1;
n = (Modulus - 1) + n;
}
modint x = *this, r = 1;
while(n) {
if(n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
constexpr modint inv() const noexcept { return pow(Modulus - 2); }
constexpr friend modint operator+(const modint &lhs, const modint &rhs) { return modint(lhs) += modint(rhs); }
constexpr friend modint operator-(const modint &lhs, const modint &rhs) { return modint(lhs) -= modint(rhs); }
constexpr friend modint operator*(const modint &lhs, const modint &rhs) { return modint(lhs) *= modint(rhs); }
constexpr friend modint operator/(const modint &lhs, const modint &rhs) { return modint(lhs) /= modint(rhs); }
constexpr friend bool operator==(const modint &lhs, const modint &rhs) { return lhs.a == rhs.a; }
constexpr friend bool operator!=(const modint &lhs, const modint &rhs) { return lhs.a != rhs.a; }
// constexpr friend modint operator^=(const modint &lhs, const modint &rhs) { return modint(lhs) ^= modint(rhs); }
};
vmint Fact{1, 1}, Ifact{1, 1};
mint inv(int n) {
if(n > MAXN) return (mint(n)).pow(MOD - 2);
if(Inv.empty()) Inv.emplace_back(0), Inv.emplace_back(1);
if(Inv.size() > n)
return Inv[n];
else {
for(int i = Inv.size(); i <= n; ++i) {
auto [y, x] = div(int(MOD), i);
Inv.emplace_back(Inv[x] * (-y));
}
return Inv[n];
}
}
mint fact(int n) {
if(Fact.size() > n)
return Fact[n];
else
for(int i = Fact.size(); i <= n; ++i) Fact.emplace_back(Fact[i - 1] * i);
return Fact[n];
}
mint ifact(int n) {
if(Ifact.size() > n)
return Ifact[n];
else
for(int i = Ifact.size(); i <= n; ++i) Ifact.emplace_back(Ifact[i - 1] * inv(i));
return Ifact[n];
}
mint modpow(ll a, ll n) { return mint(a).pow(n); }
mint inv(mint a) { return inv(a.a); }
mint ifact(mint a) { return ifact(a.a); }
mint fact(mint a) { return fact(a.a); }
mint modpow(mint a, ll n) { return modpow(a.a, n); }
mint C(int a, int b) {
if(a < 0 || b < 0) return 0;
if(a < b) return 0;
if(a > MAXN) {
mint res = 1;
rep(i, b) res *= a - i, res /= i + 1;
return res;
}
return fact(a) * ifact(b) * ifact(a - b);
}
mint P(int a, int b) {
if(a < 0 || b < 0) return 0;
if(a < b) return 0;
if(a > MAXN) {
mint res = 1;
rep(i, b) res *= a - i;
return res;
}
return fact(a) * ifact(a - b);
}
ostream &operator<<(ostream &os, mint a) {
os << a.a;
return os;
}
istream &operator>>(istream &is, mint &a) {
ll x;
is >> x;
a = x;
return is;
}
ostream &operator<<(ostream &os, const vmint &a) {
if(!a.empty()) {
os << a[0];
for(int i = 1; i < si(a); i++) os << " " << a[i];
}
return os;
}
#ifdef _MSC_VER
#include <intrin.h>
#endif
namespace convolution {
namespace internal {
int ceil_pow2(int n) {
int x = 0;
while((1U << x) < (unsigned int)(n)) x++;
return x;
}
int bsf(unsigned int n) {
#ifdef _MSC_VER
unsigned long index;
_BitScanForward(&index, n);
return index;
#else
return __builtin_ctz(n);
#endif
}
constexpr long long safe_mod(long long x, long long m) {
x %= m;
if(x < 0) x += m;
return x;
}
struct barrett {
unsigned int _m;
unsigned long long im;
barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}
unsigned int umod() const { return _m; }
unsigned int mul(unsigned int a, unsigned int b) const {
unsigned long long z = a;
z *= b;
#ifdef _MSC_VER
unsigned long long x;
_umul128(z, im, &x);
#else
unsigned long long x = (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
unsigned int v = (unsigned int)(z - x * _m);
if(_m <= v) v += _m;
return v;
}
};
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
if(m == 1) return 0;
unsigned int _m = (unsigned int)(m);
unsigned long long r = 1;
unsigned long long y = safe_mod(x, m);
while(n) {
if(n & 1) r = (r * y) % _m;
y = (y * y) % _m;
n >>= 1;
}
return r;
}
constexpr bool is_prime_constexpr(int n) {
if(n <= 1) return false;
if(n == 2 || n == 7 || n == 61) return true;
if(n % 2 == 0) return false;
long long d = n - 1;
while(d % 2 == 0) d /= 2;
for(long long a : {2, 7, 61}) {
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);
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};
long long s = b, t = a;
long long m0 = 0, m1 = 1;
while(t) {
long long u = s / t;
s -= t * u;
m0 -= m1 * u; // |m1 * u| <= |m1| * s <= b
auto tmp = s;
s = t;
t = tmp;
tmp = m0;
m0 = m1;
m1 = tmp;
}
if(m0 < 0) m0 += b / s;
return {s, m0};
}
// 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);
void butterfly(std::vector<mint> &a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if(first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for(int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for(int i = 0; i < cnt2 - 2; i++) {
sum_e[i] = es[i] * now;
now *= ies[i];
}
}
for(int ph = 1; ph <= h; ph++) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint now = 1;
for(int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for(int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p] * now;
a[i + offset] = l + r;
a[i + offset + p] = l - r;
}
now *= sum_e[bsf(~(unsigned int)(s))];
}
}
}
void butterfly_inv(std::vector<mint> &a) {
static constexpr int g = internal::primitive_root<mint::mod()>;
int n = int(a.size());
int h = internal::ceil_pow2(n);
static bool first = true;
static mint sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if(first) {
first = false;
mint es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(mint::mod() - 1);
mint e = mint(g).pow((mint::mod() - 1) >> cnt2), ie = e.inv();
for(int i = cnt2; i >= 2; i--) {
// e^(2^i) == 1
es[i - 2] = e;
ies[i - 2] = ie;
e *= e;
ie *= ie;
}
mint now = 1;
for(int i = 0; i < cnt2 - 2; i++) {
sum_ie[i] = ies[i] * now;
now *= es[i];
}
}
for(int ph = h; ph >= 1; ph--) {
int w = 1 << (ph - 1), p = 1 << (h - ph);
mint inow = 1;
for(int s = 0; s < w; s++) {
int offset = s << (h - ph + 1);
for(int i = 0; i < p; i++) {
auto l = a[i + offset];
auto r = a[i + offset + p];
a[i + offset] = l + r;
a[i + offset + p] = (unsigned long long)(mint::mod() + l.val() - r.val()) * inow.val();
}
inow *= sum_ie[bsf(~(unsigned int)(s))];
}
}
mint z = mint(n).inv();
for(int i = 0; i < n; i++) a[i] *= z;
}
} // namespace internal
std::vector<mint> convolution(std::vector<mint> a, std::vector<mint> b) {
int n = int(a.size()), m = int(b.size());
if(!n || !m) return {};
if(std::min(n, m) <= 60) {
if(n < m) {
std::swap(n, m);
std::swap(a, b);
}
std::vector<mint> ans(n + m - 1);
for(int i = 0; i < n; i++) {
for(int j = 0; j < m; j++) { ans[i + j] += a[i] * b[j]; }
}
return ans;
}
int z = 1 << internal::ceil_pow2(n + m - 1);
a.resize(z);
internal::butterfly(a);
b.resize(z);
internal::butterfly(b);
for(int i = 0; i < z; i++) { a[i] *= b[i]; }
internal::butterfly_inv(a);
a.resize(n + m - 1);
// mint iz = mint(z).inv();
// for(int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
} // namespace convolution
using Poly = vmint;
Poly low(const Poly &f, int s) { return Poly(f.begin(), f.begin() + min<int>(max(s, 1), f.size())); }
Poly operator-(Poly f) {
for(auto &&e : f) e = -e;
return f;
}
Poly &operator+=(Poly &l, const Poly &r) {
l.resize(max(l.size(), r.size()));
rep(i, r.size()) l[i] += r[i];
return l;
}
Poly operator+(Poly l, const Poly &r) { return l += r; }
Poly &operator-=(Poly &l, const Poly &r) {
l.resize(max(l.size(), r.size()));
rep(i, r.size()) l[i] -= r[i];
return l;
}
Poly operator-(Poly l, const Poly &r) { return l -= r; }
Poly &operator<<=(Poly &f, size_t n) { return f.insert(f.begin(), n, 0), f; }
Poly operator<<(Poly f, size_t n) { return f <<= n; }
Poly &operator>>=(Poly &f, size_t n) { return f.erase(f.begin(), f.begin() + min(f.size(), n)), f; }
Poly operator>>(Poly f, size_t n) { return f >>= n; }
Poly operator*(const Poly &l, const Poly &r) { return convolution::convolution(l, r); }
Poly &operator*=(Poly &l, const Poly &r) { return l = l * r; }
Poly &operator*=(Poly &l, const mint &x) {
for(auto &e : l) e *= x;
return l;
}
Poly operator*(const Poly &l, const mint &x) {
auto res = l;
return res *= x;
}
Poly inv(const Poly &f, int s = -1) {
if(s == -1) s = f.size();
Poly r(s);
r[0] = mint(1) / f[0];
for(int n = 1; n < s; n *= 2) {
auto F = low(f, 2 * n);
F.resize(2 * n);
convolution::internal::butterfly(F);
auto g = low(r, 2 * n);
g.resize(2 * n);
convolution::internal::butterfly(g);
rep(i, 2 * n) F[i] *= g[i];
convolution::internal::butterfly_inv(F);
rep(i, n) F[i] = 0;
convolution::internal::butterfly(F);
rep(i, 2 * n) F[i] *= g[i];
convolution::internal::butterfly_inv(F);
rep(i, n, min(2 * n, s)) r[i] -= F[i];
}
return r;
}
Poly integ(const Poly &f) {
Poly res(f.size() + 1);
for(int i = 1; i < (int)res.size(); ++i) res[i] = f[i - 1] / i;
return res;
}
Poly deriv(const Poly &f) {
if(f.size() == 0) return Poly();
Poly res(f.size() - 1);
rep(i, res.size()) res[i] = f[i + 1] * (i + 1);
return res;
}
Poly log(const Poly &f) {
Poly g = integ(inv(f) * deriv(f));
return Poly{g.begin(), g.begin() + f.size()};
}
Poly exp(const Poly &f) {
Poly g{1};
while(g.size() < f.size()) {
Poly x(f.begin(), f.begin() + min(f.size(), g.size() * 2));
x[0] += 1;
g.resize(2 * g.size());
x -= log(g);
x *= {g.begin(), g.begin() + g.size() / 2};
rep(i, g.size() / 2, min<int>(x.size(), g.size())) g[i] = x[i];
}
return {g.begin(), g.begin() + f.size()};
}
Poly pow(const Poly &f, ll k, int need = -1) {
const int n = (int)f.size();
if(need == -1) need = n;
int z = 0;
rep(i, n) {
if(f[i].a) break;
z++;
}
if(z * k >= need) return Poly(n);
mint rev = f[z].inv();
Poly res = exp(log((f >> z) * rev) * k) * f[z].pow(k);
res.resize(need - z * k);
return res << z * k;
}
struct Prd {
deque<Poly> deq;
Prd() = default;
void emplace(const Poly &f) { deq.emplace_back(f); }
Poly calc() {
if(deq.empty()) return {1};
sort(all(deq), [&](const Poly &f, const Poly &g) { return si(f) < si(g); });
while(deq.size() > 1) {
deq.emplace_back(deq[0] * deq[1]);
for(int i = 0; i < 2; ++i) deq.pop_front();
}
return deq.front();
}
};
Poly prd(vector<Poly> &v) {
Prd p;
for(auto &e : v) p.emplace(e);
return p.calc();
}
vmint power_table(mint x, int len) {
vmint res(len + 1);
res[0] = 1;
rep(i, len) res[i + 1] = res[i] * x;
return res;
}
// calc f(x + a)
Poly TaylorShift(Poly f, mint a) {
int n = f.size();
rep(i, n) f[i] *= fact(i);
reverse(all(f));
Poly g(n, 1);
rep(i, 1, n) g[i] = g[i - 1] * a * inv(i);
f = (f * g);
f.resize(n);
reverse(begin(f), end(f));
rep(i, n) f[i] *= ifact(i);
return f;
}
// ボールの数、一個以上必要な数、入っていなくてもいい数(区別あり)
mint choose(int num, int a, int b = 0) { return C(num + b - 1, a + b - 1); }
} // namespace modular
using namespace modular;
// https://hitonanode.github.io/cplib-cpp/number/dual_number.hpp
namespace dual_number_ {
struct has_id_method_impl {
template <class T_> static auto check(T_ *) -> decltype(T_::id(), std::true_type());
template <class T_> static auto check(...) -> std::false_type;
};
template <class T_> struct has_id : decltype(has_id_method_impl::check<T_>(nullptr)) {};
} // namespace dual_number_
// Dual number （二重数）
// Verified: https://atcoder.jp/contests/abc235/tasks/abc235_f
template <class T> struct DualNumber {
T a, b; // a + bx
template <typename T2, typename std::enable_if<dual_number_::has_id<T2>::value>::type * = nullptr> static T2 _T_id() { return T2::id(); }
template <typename T2, typename std::enable_if<!dual_number_::has_id<T2>::value>::type * = nullptr> static T2 _T_id() { return T2(1); }
DualNumber(T x = T(), T y = T()) : a(x), b(y) {}
static DualNumber id() { return DualNumber(_T_id<T>(), T()); }
explicit operator bool() const { return a != T() or b != T(); }
DualNumber operator+(const DualNumber &x) const { return DualNumber(a + x.a, b + x.b); }
DualNumber operator-(const DualNumber &x) const { return DualNumber(a - x.a, b - x.b); }
DualNumber operator*(const DualNumber &x) const { return DualNumber(a * x.a, b * x.a + a * x.b); }
DualNumber operator/(const DualNumber &x) const {
T cinv = _T_id<T>() / x.a;
return DualNumber(a * cinv, (b * x.a - a * x.b) * cinv * cinv);
}
DualNumber operator-() const { return DualNumber(-a, -b); }
DualNumber &operator+=(const DualNumber &x) { return *this = *this + x; }
DualNumber &operator-=(const DualNumber &x) { return *this = *this - x; }
DualNumber &operator*=(const DualNumber &x) { return *this = *this * x; }
DualNumber &operator/=(const DualNumber &x) { return *this = *this / x; }
bool operator==(const DualNumber &x) const { return a == x.a and b == x.b; }
bool operator!=(const DualNumber &x) const { return !(*this == x); }
bool operator<(const DualNumber &x) const { return (a != x.a ? a < x.a : b < x.b); }
// template <class OStream> friend OStream &operator<<(OStream &os, const DualNumber &x) { return os << '{' << x.a << ',' << x.b << '}'; }
};
template <class T> ostream &operator<<(ostream &os, const DualNumber<T> &d) { return os << "(" << d.a << ", " << d.b << ")"; }
using D = DualNumber<mint>;
template <typename G> struct HLDecomposition {
G &g;
vector<int> sz, in, out, head, rev, par, d, vis, roots;
HLDecomposition(G &g, vector<int> r = vector<int>())
: g(g), d(g.size()), sz(g.size()), in(g.size()), out(g.size()), head(g.size()), rev(g.size()), par(g.size()) {
if(empty(r)) {
vector<bool> vis(g.size());
for(int i = 0; i < g.size(); i++) {
if(vis[i]) continue;
roots.emplace_back(i);
queue<int> q;
q.emplace(i);
while(!empty(q)) {
int x = q.front();
vis[x] = true;
q.pop();
for(auto e : g[x]) {
if(!vis[e]) q.emplace(e);
}
}
}
} else
roots = r;
}
void dfs_sz(int idx, int p) {
par[idx] = p;
sz[idx] = 1;
if(g[idx].size() and g[idx][0] == p) swap(g[idx][0], g[idx].back());
for(auto &to : g[idx]) {
if(to == p) continue;
d[to] = d[idx] + 1;
dfs_sz(to, idx);
sz[idx] += sz[to];
if(sz[g[idx][0]] < sz[to]) swap(g[idx][0], to);
}
}
void dfs_hld(int idx, int par, int ×) {
in[idx] = times++;
rev[in[idx]] = idx;
for(auto &to : g[idx]) {
if(to == par) continue;
head[to] = (g[idx][0] == to ? head[idx] : to);
dfs_hld(to, idx, times);
}
out[idx] = times;
}
template <typename T> void dfs_hld(int idx, int par, int ×, vector<T> &v) {
in[idx] = times++;
rev[in[idx]] = idx;
for(auto &to : g[idx]) {
if(to == par) {
v[in[idx]] = to.cost;
continue;
}
head[to] = (g[idx][0] == to ? head[idx] : to);
dfs_hld(to, idx, times, v);
}
out[idx] = times;
}
template <typename T> void dfs_hld(int idx, int par, int ×, vector<T> &v, vector<T> &a) {
in[idx] = times++;
rev[in[idx]] = idx;
v[in[idx]] = a[idx];
for(auto &to : g[idx]) {
if(to == par) continue;
head[to] = (g[idx][0] == to ? head[idx] : to);
dfs_hld(to, idx, times, v, a);
}
out[idx] = times;
}
void build() {
int t = 0;
for(auto root : roots) {
head[root] = root;
dfs_sz(root, -1);
dfs_hld(root, -1, t);
}
}
template <typename T> vector<T> build(int root = 0) {
vector<T> res(g.size());
int t = 0;
for(auto root : roots) {
head[root] = root;
dfs_sz(root, -1);
dfs_hld(root, -1, t, res);
}
return res;
}
template <typename T> vector<T> build(vector<T> &a, int root = 0) {
vector<T> res(g.size());
for(auto root : roots) {
head[root] = root;
dfs_sz(root, -1);
int t = 0;
dfs_hld(root, -1, t, res, a);
}
return res;
}
int la(int v, int k) {
while(1) {
int u = head[v];
if(in[v] - k >= in[u]) return rev[in[v] - k];
k -= in[v] - in[u] + 1;
v = par[u];
}
}
int lca(int u, int v) {
for(;; v = par[head[v]]) {
if(in[u] > in[v]) swap(u, v);
if(head[u] == head[v]) return u;
}
}
template <typename T, typename Q, typename F> T query(int u, int v, const T &e, const Q &q, const F &f, bool edge = false) {
T l = e, r = e;
for(;; v = par[head[v]]) {
if(in[u] > in[v]) swap(u, v), swap(l, r);
if(head[u] == head[v]) break;
l = f(q(in[head[v]], in[v] + 1), l);
}
return f(f(q(in[u] + edge, in[v] + 1), l), r);
}
template <typename T, typename Q, typename Q2, typename F> T query(int u, int v, const T &e, const Q &q1, const Q2 &q2, const F &f, bool edge = false) {
T l = e, r = e;
for(;;) {
if(head[u] == head[v]) break;
if(in[u] > in[v]) {
l = f(l, q2(in[head[u]], in[u] + 1));
u = par[head[u]];
} else {
r = f(q1(in[head[v]], in[v] + 1), r);
v = par[head[v]];
}
}
if(in[u] > in[v]) return f(f(l, q2(in[v] + edge, in[u] + 1)), r);
return f(f(l, q1(in[u] + edge, in[v] + 1)), r);
}
template <typename Q> void add(int u, int v, const Q &q, bool edge = false) {
for(;; v = par[head[v]]) {
if(in[u] > in[v]) swap(u, v);
if(head[u] == head[v]) break;
q(in[head[v]], in[v] + 1);
}
q(in[u] + edge, in[v] + 1);
}
constexpr int operator[](int k) { return in[k]; }
constexpr int dist(int u, int v) { return d[u] + d[v] - 2 * d[lca(u, v)]; }
// u -> v の unique path
vector<int> road(int u, int v) {
int l = lca(u, v);
vector<int> a, b;
for(; v != l; v = par[v]) b.eb(v);
for(; u != l; u = par[u]) a.eb(u);
a.eb(l);
per(i, si(b), 0) a.eb(b[i]);
return a;
}
int jump(int s, int t, int i) {
if(!i) return s;
int l = lca(s, t);
int dst = d[s] + d[t] - d[l] * 2;
if(dst < i) return -1;
if(d[s] - d[l] >= i) return la(s, i);
i -= d[s] - d[l];
return la(t, d[t] - d[l] - i);
}
};
template <class T> struct VectorPool {
vector<T> pool;
vector<T *> stock;
int ptr;
VectorPool() = default;
VectorPool(int sz) : pool(sz), stock(sz) {}
inline T *alloc() { return stock[--ptr]; }
inline void free(T *t) { stock[ptr++] = t; }
void clear() {
ptr = (int)pool.size();
for(int i = 0; i < pool.size(); i++) stock[i] = &pool[i];
}
};
template <class Monoid, class OperatorMonoid = Monoid> struct RandomizedBinarySearchTree {
using F = function<Monoid(Monoid, Monoid)>;
using G = function<Monoid(Monoid, OperatorMonoid)>;
using H = function<OperatorMonoid(OperatorMonoid, OperatorMonoid)>;
using P = function<OperatorMonoid(OperatorMonoid, int)>;
inline int xor128() {
static int x = 123456789;
static int y = 362436069;
static int z = 521288629;
static int w = 88675123;
int t;
t = x ^ (x << 11);
x = y;
y = z;
z = w;
return w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
}
struct Node {
Node *l, *r;
int cnt;
Monoid key, sum;
OperatorMonoid lazy;
Node() = default;
Node(const Monoid &k, const OperatorMonoid &p) : cnt(1), key(k), sum(k), lazy(p), l(nullptr), r(nullptr) {}
};
vector<Node> pool;
int ptr;
const Monoid M1;
const OperatorMonoid OM0;
const F f;
const G g;
const H h;
const P p;
RandomizedBinarySearchTree(int sz, const F &f, const Monoid &M1) : pool(sz), ptr(0), f(f), g(G()), h(H()), p(P()), M1(M1), OM0(OperatorMonoid()) {}
RandomizedBinarySearchTree(int sz, const F &f, const G &g, const H &h, const P &p, const Monoid &M1, const OperatorMonoid &OM0)
: pool(sz), ptr(0), f(f), g(g), h(h), p(p), M1(M1), OM0(OM0) {}
inline Node *alloc(const Monoid &key) {
if(ptr == pool.size()) assert(0);
return &(pool[ptr++] = Node(key, OM0));
}
virtual Node *clone(Node *t) { return t; }
inline int count(const Node *t) { return t ? t->cnt : 0; }
inline Monoid sum(const Node *t) { return t ? t->sum : M1; }
inline Node *update(Node *t) {
t->cnt = count(t->l) + count(t->r) + 1;
t->sum = f(f(sum(t->l), t->key), sum(t->r));
return t;
}
Node *propagate(Node *t) {
t = clone(t);
if(t->lazy != OM0) {
t->key = g(t->key, p(t->lazy, 1));
if(t->l) {
t->l = clone(t->l);
t->l->lazy = h(t->l->lazy, t->lazy);
t->l->sum = g(t->l->sum, p(t->lazy, count(t->l)));
}
if(t->r) {
t->r = clone(t->r);
t->r->lazy = h(t->r->lazy, t->lazy);
t->r->sum = g(t->r->sum, p(t->lazy, count(t->r)));
}
t->lazy = OM0;
}
return update(t);
}
Node *merge(Node *l, Node *r) {
if(!l || !r) return l ? l : r;
if(xor128() % (l->cnt + r->cnt) < l->cnt) {
l = propagate(l);
l->r = merge(l->r, r);
return update(l);
} else {
r = propagate(r);
r->l = merge(l, r->l);
return update(r);
}
}
pair<Node *, Node *> split(Node *t, int k) {
if(!t) return {t, t};
t = propagate(t);
if(k <= count(t->l)) {
auto s = split(t->l, k);
t->l = s.second;
return {s.first, update(t)};
} else {
auto s = split(t->r, k - count(t->l) - 1);
t->r = s.first;
return {update(t), s.second};
}
}
Node *build(int l, int r, const vector<Monoid> &v) {
if(l + 1 >= r) return alloc(v[l]);
return merge(build(l, (l + r) >> 1, v), build((l + r) >> 1, r, v));
}
Node *build(const vector<Monoid> &v) {
ptr = 0;
return build(0, (int)v.size(), v);
}
void ddump(Node *r, typename vector<Monoid>::iterator &it) {
if(!r) return;
r = propagate(r);
ddump(r->l, it);
*it = r->key;
ddump(r->r, ++it);
}
vector<Monoid> ddump(Node *r) {
vector<Monoid> v((size_t)count(r));
auto it = begin(v);
ddump(r, it);
return v;
}
string to_string(Node *r) {
auto s = ddump(r);
string ret;
for(int i = 0; i < s.size(); i++) ret += ", ";
return (ret);
}
void insert(Node *&t, int k, const Monoid &v) {
auto x = split(t, k);
t = merge(merge(x.first, alloc(v)), x.second);
}
void erase(Node *&t, int k) {
auto x = split(t, k);
t = merge(x.first, split(x.second, 1).second);
}
Monoid query(Node *&t, int a, int b) {
auto x = split(t, a);
auto y = split(x.second, b - a);
auto ret = sum(y.first);
t = merge(x.first, merge(y.first, y.second));
return ret;
}
void set_propagate(Node *&t, int a, int b, const OperatorMonoid &p) {
auto x = split(t, a);
auto y = split(x.second, b - a);
y.first->lazy = h(y.first->lazy, p);
t = merge(x.first, merge(propagate(y.first), y.second));
}
void set_element(Node *&t, int k, const Monoid &x) {
t = propagate(t);
if(k < count(t->l))
set_element(t->l, k, x);
else if(k == count(t->l))
t->key = t->sum = x;
else
set_element(t->r, k - count(t->l) - 1, x);
t = update(t);
}
int size(Node *t) { return count(t); }
bool empty(Node *t) { return !t; }
Node *makeset() { return nullptr; }
Monoid kth_element(Node *t, int k) {
if(k < count(t->l)) return kth_element(t->l, k);
if(k == count(t->l)) return t->key;
return kth_element(t->r, k - count(t->l) - 1);
}
virtual void insert_key(Node *&t, const Monoid &x) { insert(t, lower_bound(t, x), x); }
int lower_bound(Node *t, const Monoid &x) {
if(!t) return 0;
if(!(t->key < x)) return lower_bound(t->l, x);
return lower_bound(t->r, x) + count(t->l) + 1;
}
};
struct S {
D d;
int x;
mint sum, sum2;
const bool operator<(const S &r) const { return x < r.x; }
};
ostream &operator<<(ostream &os, S s) {
return os << "{"
<< "(" << s.d.a << ", " << s.d.b << "), " << s.x << ", " << s.sum << ", " << s.sum2 << "}";
}
int main() {
INT(n);
VEC(int, a, n);
auto g = getG(n);
HLDecomposition hld(g);
hld.build();
auto F = [](S x, S y) { return S{x.d + y.d, max(x.x, y.x), x.sum + y.sum, x.sum2 + y.sum2}; };
auto G = [](S x, D y) { return S{x.d * y, x.x, x.sum * y.a + x.sum2 * y.b, x.sum2 * y.a}; };
auto H = [](D x, D y) { return x * y; };
auto P = [](D x, int) { return x; };
RandomizedBinarySearchTree<S, D> s(n * 22, F, G, H, P, S{D(), 0, 0}, D(1, 0));
mint ans;
auto insert = [&](decltype(s)::Node *&n, const S &x) {
int k = s.lower_bound(n, x);
if(k == s.count(n))
s.insert(n, k, x);
else {
auto y = s.kth_element(n, k);
// dump(x, y);
if(y.x == x.x)
s.set_element(n, k, F(x, y));
else {
s.insert(n, k, x);
// dump(s.count(n));
}
}
};
vector<decltype(s)::Node *> nodes(n);
REC([&](auto &&f, int x, int p) -> void {
auto &res = nodes[x];
res = s.makeset();
s.insert(res, 0, S{D(1, 1), a[x], a[x], a[x]});
fore(e, g[x]) {
if(e == p) continue;
f(e, x);
auto &v = nodes[e];
if(s.count(res) < s.count(v)) swap(res, v);
// dump(s.ddump(nodes[1]));
vector<S> w = s.ddump(v);
dump(w, s.ddump(res));
vector<S> nxt;
int pre = -1;
D d{};
fore(e, w) d += e.d;
per(i, si(w)) {
int l = (pre == -1 ? s.lower_bound(res, w[i]) : pre);
// dump(s.lower_bound(res, w[i]));
// dump(s.ddump(res));
int r = (i == si(w) - 1 ? s.count(res) : s.lower_bound(res, w[i + 1]));
pre = r;
// dump(l, r, d);
if(l < r) s.set_propagate(res, l, r, d);
nxt.eb(G(w[i], s.query(res, 0, l).d));
d -= w[i].d;
}
while(s.count(res) and s.kth_element(res, 0).x < w[0].x) s.erase(res, 0);
dump(s.ddump(res));
fore(e, nxt) insert(res, e);
dump(x, (int)e, s.ddump(res));
}
mint K = mint(2).pow(n - 1 - hld.sz[x]);
if(p == -1) K = 1;
ans += K * s.query(res, 0, s.count(res)).sum;
auto now = S{D(mint(2).pow(hld.sz[x] - 1), 0), 0, 0, 0};
s.insert(res, 0, now);
dump(x, s.ddump(res));
dump(ans);
// dump(s.ddump(nodes[1]));
// return res;
})
(0, -1);
// fore(x, y, res) {
// dump(x, y.a, y.b);
// ans += x * y.b;
// }
OUT(ans);
}