結果
| 問題 |
No.3315 FPS Game
|
| コンテスト | |
| ユーザー |
 hitonanode
|
| 提出日時 | 2025-10-24 22:35:49 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 200 ms / 3,250 ms |
| コード長 | 34,569 bytes |
| コンパイル時間 | 4,878 ms |
| コンパイル使用メモリ | 292,172 KB |
| 実行使用メモリ | 34,144 KB |
| 最終ジャッジ日時 | 2025-10-24 22:36:00 |
| 合計ジャッジ時間 | 9,910 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 25 |
ソースコード
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <optional>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif
#include <utility>
#include <vector>
// lowest common ancestor (LCA) for undirected weighted tree
template <typename T> struct UndirectedWeightedTree {
int INVALID = -1;
int V, lgV;
int E;
int root;
std::vector<std::vector<std::pair<int, int>>> adj; // (nxt_vertex, edge_id)
// vector<pint> edge; // edges[edge_id] = (vertex_id, vertex_id)
std::vector<T> weight; // w[edge_id]
std::vector<int> par; // parent_vertex_id[vertex_id]
std::vector<int> depth; // depth_from_root[vertex_id]
std::vector<T> acc_weight; // w_sum_from_root[vertex_id]
void _fix_root_dfs(int now, int prv, int prv_edge_id) {
par[now] = prv;
if (prv_edge_id != INVALID) acc_weight[now] = acc_weight[prv] + weight[prv_edge_id];
for (auto nxt : adj[now])
if (nxt.first != prv) {
depth[nxt.first] = depth[now] + 1;
_fix_root_dfs(nxt.first, now, nxt.second);
}
}
UndirectedWeightedTree() = default;
UndirectedWeightedTree(int N) : V(N), E(0), adj(N) {
lgV = 1;
while (1 << lgV < V) lgV++;
}
void add_edge(int u, int v, T w) {
adj[u].emplace_back(v, E);
adj[v].emplace_back(u, E);
// edge.emplace_back(u, v);
weight.emplace_back(w);
E++;
}
std::vector<std::vector<int>> doubling;
void _doubling_precalc() {
doubling.assign(lgV, std::vector<int>(V));
doubling[0] = par;
for (int d = 0; d < lgV - 1; d++)
for (int i = 0; i < V; i++) {
if (doubling[d][i] == INVALID)
doubling[d + 1][i] = INVALID;
else
doubling[d + 1][i] = doubling[d][doubling[d][i]];
}
}
void fix_root(int r) {
root = r;
par.resize(V);
depth.resize(V);
depth[r] = 0;
acc_weight.resize(V);
acc_weight[r] = 0;
_fix_root_dfs(root, INVALID, INVALID);
_doubling_precalc();
}
int kth_parent(int x, int k) const {
if (depth[x] < k) return INVALID;
for (int d = 0; d < lgV; d++) {
if (x == INVALID) return INVALID;
if (k & (1 << d)) x = doubling[d][x];
}
return x;
}
int lowest_common_ancestor(int u, int v) const {
if (depth[u] > depth[v]) std::swap(u, v);
v = kth_parent(v, depth[v] - depth[u]);
if (u == v) return u;
for (int d = lgV - 1; d >= 0; d--) {
if (doubling[d][u] != doubling[d][v]) u = doubling[d][u], v = doubling[d][v];
}
return par[u];
}
T path_length(int u, int v) const {
// Not distance, but the sum of weights
int r = lowest_common_ancestor(u, v);
return (acc_weight[u] - acc_weight[r]) + (acc_weight[v] - acc_weight[r]);
}
int s_to_t_by_k_steps(int s, int t, int k) const {
int l = lowest_common_ancestor(s, t);
int dsl = depth[s] - depth[l], dtl = depth[t] - depth[l];
if (k > dsl + dtl) {
return INVALID;
} else if (k < dsl) {
return kth_parent(s, k);
} else if (k == dsl) {
return l;
} else {
return kth_parent(t, dsl + dtl - k);
}
}
};
#include <algorithm>
#include <cassert>
#include <deque>
#include <fstream>
#include <functional>
#include <limits>
#include <queue>
#include <string>
#include <tuple>
#include <utility>
#include <vector>
template <typename T, T INF = std::numeric_limits<T>::max() / 2, int INVALID = -1>
struct shortest_path {
int V, E;
bool single_positive_weight;
T wmin, wmax;
std::vector<std::pair<int, T>> tos;
std::vector<int> head;
std::vector<std::tuple<int, int, T>> edges;
void build_() {
if (int(tos.size()) == E and int(head.size()) == V + 1) return;
tos.resize(E);
head.assign(V + 1, 0);
for (const auto &e : edges) ++head[std::get<0>(e) + 1];
for (int i = 0; i < V; ++i) head[i + 1] += head[i];
auto cur = head;
for (const auto &e : edges) {
tos[cur[std::get<0>(e)]++] = std::make_pair(std::get<1>(e), std::get<2>(e));
}
}
shortest_path(int V = 0) : V(V), E(0), single_positive_weight(true), wmin(0), wmax(0) {}
void add_edge(int s, int t, T w) {
assert(0 <= s and s < V);
assert(0 <= t and t < V);
edges.emplace_back(s, t, w);
++E;
if (w > 0 and wmax > 0 and wmax != w) single_positive_weight = false;
wmin = std::min(wmin, w);
wmax = std::max(wmax, w);
}
void add_bi_edge(int u, int v, T w) {
add_edge(u, v, w);
add_edge(v, u, w);
}
std::vector<T> dist;
std::vector<int> prev;
// Dijkstra algorithm
// - Requirement: wmin >= 0
// - Complexity: O(E log E)
using Pque = std::priority_queue<std::pair<T, int>, std::vector<std::pair<T, int>>,
std::greater<std::pair<T, int>>>;
template <class Heap = Pque> void dijkstra(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF);
prev.assign(V, INVALID);
dist[s] = 0;
Heap pq;
pq.emplace(0, s);
while (!pq.empty()) {
T d;
int v;
std::tie(d, v) = pq.top();
pq.pop();
if (t == v) return;
if (dist[v] < d) continue;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = d + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
pq.emplace(dnx, nx.first);
}
}
}
}
// Dijkstra algorithm
// - Requirement: wmin >= 0
// - Complexity: O(V^2 + E)
void dijkstra_vquad(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF);
prev.assign(V, INVALID);
dist[s] = 0;
std::vector<char> fixed(V, false);
while (true) {
int r = INVALID;
T dr = INF;
for (int i = 0; i < V; i++) {
if (!fixed[i] and dist[i] < dr) r = i, dr = dist[i];
}
if (r == INVALID or r == t) break;
fixed[r] = true;
int nxt;
T dx;
for (int e = head[r]; e < head[r + 1]; ++e) {
std::tie(nxt, dx) = tos[e];
if (dist[nxt] > dist[r] + dx) dist[nxt] = dist[r] + dx, prev[nxt] = r;
}
}
}
// Bellman-Ford algorithm
// - Requirement: no negative loop
// - Complexity: O(VE)
bool bellman_ford(int s, int nb_loop) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
for (int l = 0; l < nb_loop; l++) {
bool upd = false;
for (int v = 0; v < V; v++) {
if (dist[v] == INF) continue;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[v] + nx.second;
if (dist[nx.first] > dnx) dist[nx.first] = dnx, prev[nx.first] = v, upd = true;
}
}
if (!upd) return true;
}
return false;
}
// Bellman-ford algorithm using deque
// - Requirement: no negative loop
// - Complexity: O(VE)
void spfa(int s) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF);
prev.assign(V, INVALID);
dist[s] = 0;
std::deque<int> q;
std::vector<char> in_queue(V);
q.push_back(s), in_queue[s] = 1;
while (!q.empty()) {
int now = q.front();
q.pop_front(), in_queue[now] = 0;
for (int e = head[now]; e < head[now + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[now] + nx.second;
int nxt = nx.first;
if (dist[nxt] > dnx) {
dist[nxt] = dnx;
if (!in_queue[nxt]) {
if (q.size() and dnx < dist[q.front()]) { // Small label first optimization
q.push_front(nxt);
} else {
q.push_back(nxt);
}
prev[nxt] = now, in_queue[nxt] = 1;
}
}
}
}
}
// 01-BFS
// - Requirement: all weights must be 0 or w (positive constant).
// - Complexity: O(V + E)
void zero_one_bfs(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
std::vector<int> q(V * 4);
int ql = V * 2, qr = V * 2;
q[qr++] = s;
while (ql < qr) {
int v = q[ql++];
if (v == t) return;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[v] + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
if (nx.second) {
q[qr++] = nx.first;
} else {
q[--ql] = nx.first;
}
}
}
}
}
// Dial's algorithm
// - Requirement: wmin >= 0
// - Complexity: O(wmax * V + E)
void dial(int s, int t = INVALID) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
std::vector<std::vector<std::pair<int, T>>> q(wmax + 1);
q[0].emplace_back(s, dist[s]);
int ninq = 1;
int cur = 0;
T dcur = 0;
for (; ninq; ++cur, ++dcur) {
if (cur == wmax + 1) cur = 0;
while (!q[cur].empty()) {
int v = q[cur].back().first;
T dnow = q[cur].back().second;
q[cur].pop_back(), --ninq;
if (v == t) return;
if (dist[v] < dnow) continue;
for (int e = head[v]; e < head[v + 1]; ++e) {
const auto &nx = tos[e];
T dnx = dist[v] + nx.second;
if (dist[nx.first] > dnx) {
dist[nx.first] = dnx, prev[nx.first] = v;
int nxtcur = cur + int(nx.second);
if (nxtcur >= int(q.size())) nxtcur -= q.size();
q[nxtcur].emplace_back(nx.first, dnx), ++ninq;
}
}
}
}
}
// Solver for DAG
// - Requirement: graph is DAG
// - Complexity: O(V + E)
bool dag_solver(int s) {
assert(0 <= s and s < V);
build_();
dist.assign(V, INF), prev.assign(V, INVALID);
dist[s] = 0;
std::vector<int> indeg(V, 0);
std::vector<int> q(V * 2);
int ql = 0, qr = 0;
q[qr++] = s;
while (ql < qr) {
int now = q[ql++];
for (int e = head[now]; e < head[now + 1]; ++e) {
const auto &nx = tos[e];
++indeg[nx.first];
if (indeg[nx.first] == 1) q[qr++] = nx.first;
}
}
ql = qr = 0;
q[qr++] = s;
while (ql < qr) {
int now = q[ql++];
for (int e = head[now]; e < head[now + 1]; ++e) {
const auto &nx = tos[e];
--indeg[nx.first];
if (dist[nx.first] > dist[now] + nx.second)
dist[nx.first] = dist[now] + nx.second, prev[nx.first] = now;
if (indeg[nx.first] == 0) q[qr++] = nx.first;
}
}
return *max_element(indeg.begin(), indeg.end()) == 0;
}
// Retrieve a sequence of vertex ids that represents shortest path [s, ..., goal]
// If not reachable to goal, return {}
std::vector<int> retrieve_path(int goal) const {
assert(int(prev.size()) == V);
assert(0 <= goal and goal < V);
if (dist[goal] == INF) return {};
std::vector<int> ret{goal};
while (prev[goal] != INVALID) {
goal = prev[goal];
ret.push_back(goal);
}
std::reverse(ret.begin(), ret.end());
return ret;
}
void solve(int s, int t = INVALID) {
if (wmin >= 0) {
if (single_positive_weight) {
zero_one_bfs(s, t);
} else if (wmax <= 10) {
dial(s, t);
} else {
if ((long long)V * V < (E << 4)) {
dijkstra_vquad(s, t);
} else {
dijkstra(s, t);
}
}
} else {
bellman_ford(s, V);
}
}
// Warshall-Floyd algorithm
// - Requirement: no negative loop
// - Complexity: O(E + V^3)
std::vector<std::vector<T>> floyd_warshall() {
build_();
std::vector<std::vector<T>> dist2d(V, std::vector<T>(V, INF));
for (int i = 0; i < V; i++) {
dist2d[i][i] = 0;
for (const auto &e : edges) {
int s = std::get<0>(e), t = std::get<1>(e);
dist2d[s][t] = std::min(dist2d[s][t], std::get<2>(e));
}
}
for (int k = 0; k < V; k++) {
for (int i = 0; i < V; i++) {
if (dist2d[i][k] == INF) continue;
for (int j = 0; j < V; j++) {
if (dist2d[k][j] == INF) continue;
dist2d[i][j] = std::min(dist2d[i][j], dist2d[i][k] + dist2d[k][j]);
}
}
}
return dist2d;
}
void to_dot(std::string filename = "shortest_path") const {
std::ofstream ss(filename + ".DOT");
ss << "digraph{\n";
build_();
for (int i = 0; i < V; i++) {
for (int e = head[i]; e < head[i + 1]; ++e) {
ss << i << "->" << tos[e].first << "[label=" << tos[e].second << "];\n";
}
}
ss << "}\n";
ss.close();
return;
}
};
#include <cassert>
#include <iostream>
#include <set>
#include <vector>
template <int md> struct ModInt {
static_assert(md > 1);
using lint = long long;
constexpr static int mod() { return md; }
static int get_primitive_root() {
static int primitive_root = 0;
if (!primitive_root) {
primitive_root = [&]() {
std::set<int> fac;
int v = md - 1;
for (lint i = 2; i * i <= v; i++)
while (v % i == 0) fac.insert(i), v /= i;
if (v > 1) fac.insert(v);
for (int g = 1; g < md; g++) {
bool ok = true;
for (auto i : fac)
if (ModInt(g).pow((md - 1) / i) == 1) {
ok = false;
break;
}
if (ok) return g;
}
return -1;
}();
}
return primitive_root;
}
int val_;
int val() const noexcept { return val_; }
constexpr ModInt() : val_(0) {}
constexpr ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; }
constexpr ModInt(lint v) { _setval(v % md + md); }
constexpr explicit operator bool() const { return val_ != 0; }
constexpr ModInt operator+(const ModInt &x) const {
return ModInt()._setval((lint)val_ + x.val_);
}
constexpr ModInt operator-(const ModInt &x) const {
return ModInt()._setval((lint)val_ - x.val_ + md);
}
constexpr ModInt operator*(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.val_ % md);
}
constexpr ModInt operator/(const ModInt &x) const {
return ModInt()._setval((lint)val_ * x.inv().val() % md);
}
constexpr ModInt operator-() const { return ModInt()._setval(md - val_); }
constexpr ModInt &operator+=(const ModInt &x) { return *this = *this + x; }
constexpr ModInt &operator-=(const ModInt &x) { return *this = *this - x; }
constexpr ModInt &operator*=(const ModInt &x) { return *this = *this * x; }
constexpr ModInt &operator/=(const ModInt &x) { return *this = *this / x; }
friend constexpr ModInt operator+(lint a, const ModInt &x) { return ModInt(a) + x; }
friend constexpr ModInt operator-(lint a, const ModInt &x) { return ModInt(a) - x; }
friend constexpr ModInt operator*(lint a, const ModInt &x) { return ModInt(a) * x; }
friend constexpr ModInt operator/(lint a, const ModInt &x) { return ModInt(a) / x; }
constexpr bool operator==(const ModInt &x) const { return val_ == x.val_; }
constexpr bool operator!=(const ModInt &x) const { return val_ != x.val_; }
constexpr bool operator<(const ModInt &x) const {
return val_ < x.val_;
} // To use std::map<ModInt, T>
friend std::istream &operator>>(std::istream &is, ModInt &x) {
lint t;
return is >> t, x = ModInt(t), is;
}
constexpr friend std::ostream &operator<<(std::ostream &os, const ModInt &x) {
return os << x.val_;
}
constexpr ModInt pow(lint n) const {
ModInt ans = 1, tmp = *this;
while (n) {
if (n & 1) ans *= tmp;
tmp *= tmp, n >>= 1;
}
return ans;
}
static constexpr int cache_limit = std::min(md, 1 << 21);
static std::vector<ModInt> facs, facinvs, invs;
constexpr static void _precalculation(int N) {
const int l0 = facs.size();
if (N > md) N = md;
if (N <= l0) return;
facs.resize(N), facinvs.resize(N), invs.resize(N);
for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i;
facinvs[N - 1] = facs.back().pow(md - 2);
for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1);
for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1];
}
constexpr ModInt inv() const {
if (this->val_ < cache_limit) {
if (facs.empty()) facs = {1}, facinvs = {1}, invs = {0};
while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2);
return invs[this->val_];
} else {
return this->pow(md - 2);
}
}
constexpr static ModInt fac(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
while (n >= int(facs.size())) _precalculation(facs.size() * 2);
return facs[n];
}
constexpr static ModInt facinv(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
while (n >= int(facs.size())) _precalculation(facs.size() * 2);
return facinvs[n];
}
constexpr static ModInt doublefac(int n) {
assert(n >= 0);
if (n >= md) return ModInt(0);
long long k = (n + 1) / 2;
return (n & 1) ? ModInt::fac(k * 2) / (ModInt(2).pow(k) * ModInt::fac(k))
: ModInt::fac(k) * ModInt(2).pow(k);
}
constexpr static ModInt nCr(int n, int r) {
assert(n >= 0);
if (r < 0 or n < r) return ModInt(0);
return ModInt::fac(n) * ModInt::facinv(r) * ModInt::facinv(n - r);
}
constexpr static ModInt nPr(int n, int r) {
assert(n >= 0);
if (r < 0 or n < r) return ModInt(0);
return ModInt::fac(n) * ModInt::facinv(n - r);
}
static ModInt binom(long long n, long long r) {
static long long bruteforce_times = 0;
if (r < 0 or n < r) return ModInt(0);
if (n <= bruteforce_times or n < (int)facs.size()) return ModInt::nCr(n, r);
r = std::min(r, n - r);
assert((int)r == r);
ModInt ret = ModInt::facinv(r);
for (int i = 0; i < r; ++i) ret *= n - i;
bruteforce_times += r;
return ret;
}
// Multinomial coefficient, (k_1 + k_2 + ... + k_m)! / (k_1! k_2! ... k_m!)
// Complexity: O(sum(ks))
// Verify: https://yukicoder.me/problems/no/3178
template <class Vec> static ModInt multinomial(const Vec &ks) {
ModInt ret{1};
int sum = 0;
for (int k : ks) {
assert(k >= 0);
ret *= ModInt::facinv(k), sum += k;
}
return ret * ModInt::fac(sum);
}
template <class... Args> static ModInt multinomial(Args... args) {
int sum = (0 + ... + args);
ModInt result = (1 * ... * ModInt::facinv(args));
return ModInt::fac(sum) * result;
}
// Catalan number, C_n = binom(2n, n) / (n + 1) = # of Dyck words of length 2n
// C_0 = 1, C_1 = 1, C_2 = 2, C_3 = 5, C_4 = 14, ...
// https://oeis.org/A000108
// Complexity: O(n)
static ModInt catalan(int n) {
if (n < 0) return ModInt(0);
return ModInt::fac(n * 2) * ModInt::facinv(n + 1) * ModInt::facinv(n);
}
ModInt sqrt() const {
if (val_ == 0) return 0;
if (md == 2) return val_;
if (pow((md - 1) / 2) != 1) return 0;
ModInt b = 1;
while (b.pow((md - 1) / 2) == 1) b += 1;
int e = 0, m = md - 1;
while (m % 2 == 0) m >>= 1, e++;
ModInt x = pow((m - 1) / 2), y = (*this) * x * x;
x *= (*this);
ModInt z = b.pow(m);
while (y != 1) {
int j = 0;
ModInt t = y;
while (t != 1) j++, t *= t;
z = z.pow(1LL << (e - j - 1));
x *= z, z *= z, y *= z;
e = j;
}
return ModInt(std::min(x.val_, md - x.val_));
}
};
template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1};
template <int md> std::vector<ModInt<md>> ModInt<md>::invs = {0};
using mint = ModInt<998244353>;
#include <algorithm>
#include <array>
#include <cassert>
#include <tuple>
#include <vector>
// Integer convolution for arbitrary mod
// with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class.
// We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`.
// input: a (size: n), b (size: m)
// return: vector (size: n + m - 1)
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner);
constexpr int nttprimes[3] = {998244353, 167772161, 469762049};
// Integer FFT (Fast Fourier Transform) for ModInt class
// (Also known as Number Theoretic Transform, NTT)
// is_inverse: inverse transform
// ** Input size must be 2^n **
template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) {
int n = a.size();
if (n == 1) return;
static const int mod = MODINT::mod();
static const MODINT root = MODINT::get_primitive_root();
assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0);
static std::vector<MODINT> w{1}, iw{1};
for (int m = w.size(); m < n / 2; m *= 2) {
MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw;
w.resize(m * 2), iw.resize(m * 2);
for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv;
}
if (!is_inverse) {
for (int m = n; m >>= 1;) {
for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
for (int i = s; i < s + m; i++) {
MODINT x = a[i], y = a[i + m] * w[k];
a[i] = x + y, a[i + m] = x - y;
}
}
}
} else {
for (int m = 1; m < n; m *= 2) {
for (int s = 0, k = 0; s < n; s += 2 * m, k++) {
for (int i = s; i < s + m; i++) {
MODINT x = a[i], y = a[i + m];
a[i] = x + y, a[i + m] = (x - y) * iw[k];
}
}
}
int n_inv = MODINT(n).inv().val();
for (auto &v : a) v *= n_inv;
}
}
template <int MOD>
std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) {
int sz = a.size();
assert(a.size() == b.size() and __builtin_popcount(sz) == 1);
std::vector<ModInt<MOD>> ap(sz), bp(sz);
for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i];
ntt(ap, false);
if (a == b)
bp = ap;
else
ntt(bp, false);
for (int i = 0; i < sz; i++) ap[i] *= bp[i];
ntt(ap, true);
return ap;
}
long long garner_ntt_(int r0, int r1, int r2, int mod) {
using mint2 = ModInt<nttprimes[2]>;
static const long long m01 = 1LL * nttprimes[0] * nttprimes[1];
static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv().val();
static const long long m01_inv_m2 = mint2(m01).inv().val();
int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1];
auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2;
return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val()) % mod;
}
template <typename MODINT>
std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) {
if (a.empty() or b.empty()) return {};
int sz = 1, n = a.size(), m = b.size();
while (sz < n + m) sz <<= 1;
if (sz <= 16) {
std::vector<MODINT> ret(n + m - 1);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j];
}
return ret;
}
int mod = MODINT::mod();
if (skip_garner or
std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) {
a.resize(sz), b.resize(sz);
if (a == b) {
ntt(a, false);
b = a;
} else {
ntt(a, false), ntt(b, false);
}
for (int i = 0; i < sz; i++) a[i] *= b[i];
ntt(a, true);
a.resize(n + m - 1);
} else {
std::vector<int> ai(sz), bi(sz);
for (int i = 0; i < n; i++) ai[i] = a[i].val();
for (int i = 0; i < m; i++) bi[i] = b[i].val();
auto ntt0 = nttconv_<nttprimes[0]>(ai, bi);
auto ntt1 = nttconv_<nttprimes[1]>(ai, bi);
auto ntt2 = nttconv_<nttprimes[2]>(ai, bi);
a.resize(n + m - 1);
for (int i = 0; i < n + m - 1; i++)
a[i] = garner_ntt_(ntt0[i].val(), ntt1[i].val(), ntt2[i].val(), mod);
}
return a;
}
template <typename MODINT>
std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) {
return nttconv<MODINT>(a, b, false);
}
int main() {
int N, S, T;
cin >> N >> S >> T;
--S, --T;
UndirectedWeightedTree<int> tree(N);
shortest_path<int> sp(N);
vector<pint> edges(N - 1);
vector<int> deg(N);
for (auto &[a, b] : edges) {
cin >> a >> b;
--a, --b;
tree.add_edge(a, b, 1);
sp.add_bi_edge(a, b, 1);
deg.at(a)++;
deg.at(b)++;
}
dbg(edges);
tree.fix_root(0);
auto [s0, s1] = edges.at(S);
auto [t0, t1] = edges.at(T);
if (tree.path_length(s0, t0) > tree.path_length(s1, t0)) swap(s0, s1);
if (tree.path_length(s0, t0) > tree.path_length(s0, t1)) swap(t0, t1);
sp.solve(s0, t0);
const auto path = sp.retrieve_path(t0);
dbg(path);
vector<int> dseq;
for (int p : path) dseq.push_back(deg.at(p) - 2);
dbg(dseq);
auto rec = [&](auto &&self, int l, int r) -> vector<mint> {
if (l + 1 == r) {
const int n = dseq.at(l);
vector<mint> ret(n + 2);
REP(k, n + 1) ret.at(k + 1) = mint::nPr(n, k);
return ret;
}
const int mid = (l + r) / 2;
return nttconv(self(self, l, mid), self(self, mid, r));
};
auto ret = rec(rec, 0, dseq.size());
ret.resize(N);
dbg(ret);
for (auto e : ret) cout << e << ' ';
cout << '\n';
}