結果
| 問題 |
No.3315 FPS Game
|
| コンテスト | |
| ユーザー |
 dyktr_06
|
| 提出日時 | 2025-10-24 23:28:24 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 386 ms / 3,250 ms |
| コード長 | 36,157 bytes |
| コンパイル時間 | 4,293 ms |
| コンパイル使用メモリ | 261,600 KB |
| 実行使用メモリ | 48,024 KB |
| 最終ジャッジ日時 | 2025-10-24 23:28:39 |
| 合計ジャッジ時間 | 11,429 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge2 |
（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 <bits/stdc++.h>
using namespace std;
#define overload4(_1, _2, _3, _4, name, ...) name
#define rep1(n) for(int i = 0; i < (int)(n); ++i)
#define rep2(i, n) for(int i = 0; i < (int)(n); ++i)
#define rep3(i, a, b) for(int i = (a); i < (int)(b); ++i)
#define rep4(i, a, b, c) for(int i = (a); i < (int)(b); i += (c))
#define rep(...) overload4(__VA_ARGS__, rep4, rep3, rep2, rep1)(__VA_ARGS__)
#define rrep(i,n) for(int i = (int)(n) - 1; i >= 0; --i)
#define ALL(a) (a).begin(), (a).end()
#define Sort(a) (sort((a).begin(), (a).end()))
#define RSort(a) (sort((a).rbegin(), (a).rend()))
#define UNIQUE(a) (a.erase(unique((a).begin(), (a).end()), (a).end()))
using i64 = int64_t;
using i128 = __int128_t;
using ll = long long;
using ul = unsigned long long;
using ull = unsigned long long;
using ld = long double;
using vi = vector<int>;
using vll = vector<long long>;
using vull = vector<unsigned long long>;
using vc = vector<char>;
using vst = vector<string>;
using vd = vector<double>;
using vld = vector<long double>;
using P = pair<long long, long long>;
template<class T> long long sum(const T &a){ return accumulate(a.begin(), a.end(), 0LL); }
template<class T> auto min(const T &a){ return *min_element(a.begin(), a.end()); }
template<class T> auto max(const T &a){ return *max_element(a.begin(), a.end()); }
const long long MINF = 0x7fffffffffff;
const long long INF = 0x1fffffffffffffff;
const long long MOD = 998244353;
const long double EPS = 1e-9;
const long double PI = acos(-1);
template<class T> inline bool chmax(T &a, T b) { if(a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T &a, T b) { if(a > b) { a = b; return 1; } return 0; }
template<typename T1, typename T2> istream &operator>>(istream &is, pair<T1, T2> &p){ is >> p.first >> p.second; return is; }
template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){ os << "(" << p.first << ", " << p.second << ")"; return os; }
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for(T &in : v) is >> in; return is; }
template<typename T> ostream &operator<<(ostream &os, const vector<T> &v){ for(int i = 0; i < (int) v.size(); ++i){ os << v[i] << (i + 1 != (int) v.size() ? " " : ""); } return os; }
template <typename T, typename S> ostream &operator<<(ostream &os, const map<T, S> &mp){ for(auto &[key, val] : mp){ os << key << ":" << val << " "; } return os; }
template <typename T> ostream &operator<<(ostream &os, const set<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, const multiset<T> &st){ auto itr = st.begin(); for(int i = 0; i < (int) st.size(); ++i){ os << *itr << (i + 1 != (int) st.size() ? " " : ""); itr++; } return os; }
template <typename T> ostream &operator<<(ostream &os, queue<T> q){ while(q.size()){ os << q.front() << " "; q.pop(); } return os; }
template <typename T> ostream &operator<<(ostream &os, deque<T> q){ while(q.size()){ os << q.front() << " "; q.pop_front(); } return os; }
template <typename T> ostream &operator<<(ostream &os, stack<T> st){ while(st.size()){ os << st.top() << " "; st.pop(); } return os; }
template <class T, class Container, class Compare> ostream &operator<<(ostream &os, priority_queue<T, Container, Compare> pq){ while(pq.size()){ os << pq.top() << " "; pq.pop(); } return os; }
template<class T, class U>
void inGraph(vector<vector<T>> &G, U n, U m, bool directed = true, bool zero_index = true){
G.resize(n);
for(int i = 0; i < m; i++){
int a, b;
cin >> a >> b;
if(!zero_index) a--, b--;
G[a].push_back(b);
if(!directed) G[b].push_back(a);
}
}
template <typename T>
long long binary_search(long long ok, long long ng, T check){
while(abs(ok - ng) > 1){
long long mid = (ok + ng) / 2;
if(check(mid)) ok = mid;
else ng = mid;
}
return ok;
}
template <typename T>
long double binary_search_real(long double ok, long double ng, T check, int iter = 100){
for(int i = 0; i < iter; ++i){
long double mid = (ok + ng) / 2;
if(check(mid)) ok = mid;
else ng = mid;
}
return ok;
}
long long trisum(long long a, long long b){
if(a > b) return 0;
long long res = ((b - a + 1) * (a + b)) / 2;
return res;
}
template <typename T>
T intpow(T x, int n){
T ret = 1;
while(n > 0) {
if(n & 1) (ret *= x);
(x *= x);
n >>= 1;
}
return ret;
}
template <typename T>
T getDivision(T a, T b){
if(b == 0) return -1;
if(a >= 0 && b > 0){
return a / b;
} else if(a < 0 && b > 0){
return a / b - (a % b != 0);
} else if(a >= 0 && b < 0){
return a / b;
} else{
return a / b + (a % b != 0);
}
}
template <typename T>
T getReminder(T a, T b){
if(b == 0) return -1;
if(a >= 0 && b > 0){
return a % b;
} else if(a < 0 && b > 0){
return ((a % b) + b) % b;
} else if(a >= 0 && b < 0){
return a % b;
} else{
return (abs(b) - abs(a % b)) % b;
}
}
template<class T, class U> inline T vin(T &vec, U n) { vec.resize(n); for(int i = 0; i < (int) n; ++i) cin >> vec[i]; return vec; }
template<class T> inline void vout(T vec, string s = "\n"){ for(auto x : vec) cout << x << s; }
template<class... T> void in(T&... a){ (cin >> ... >> a); }
void out(){ cout << '\n'; }
template<class T, class... Ts> void out(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
void fout(){ cout << endl; }
template<class T, class... Ts> void fout(const T &a, const Ts&... b){ cout << a; (cout << ... << (cout << ' ', b)); cout << endl; }
void debug(){ cerr << '\n'; }
template<class T, class... Ts> void debug(const T &a, const Ts&... b){ cerr << a; (cerr << ... << (cerr << ' ', b)); cerr << '\n'; }
class HeavyLightDecomposition{
protected:
int V;
vector<vector<int>> G;
vector<int> stsize, parent, pathtop, depth, in, reverse_in, out;
int root;
private:
// Subtree Size
void buildStsize(int curr, int prev){
stsize[curr] = 1, parent[curr] = prev;
for(int &v : G[curr]){
if(v == prev){
if(v == G[curr].back()) break;
else swap(v, G[curr].back());
}
buildStsize(v, curr);
stsize[curr] += stsize[v];
if(stsize[v] > stsize[G[curr][0]]){
swap(v, G[curr][0]);
}
}
}
void buildPath(int curr, int prev, int &t){
in[curr] = t++;
reverse_in[in[curr]] = curr;
for(int v : G[curr]){
if(v == prev) continue;
if(v == G[curr][0]){
pathtop[v] = pathtop[curr];
} else{
pathtop[v] = v;
}
depth[v] = depth[curr] + 1;
buildPath(v, curr, t);
}
out[curr] = t;
}
public:
HeavyLightDecomposition(int node_size) : V(node_size), G(V), stsize(V, 0), parent(V, -1),
pathtop(V, -1), depth(V, 0), in(V, -1), reverse_in(V, -1), out(V, -1){}
void add_edge(int u, int v){
G[u].push_back(v);
G[v].push_back(u);
}
void build(int _root = 0){
root = _root;
int t = 0;
buildStsize(root, -1);
pathtop[root] = root;
buildPath(root, -1, t);
}
inline int get(int a){
return in[a];
}
int la(int a, int k) {
while(true){
int u = pathtop[a];
if(in[a] - k >= in[u]) return reverse_in[in[a] - k];
k -= in[a] - in[u] + 1;
a = parent[u];
}
}
int lca(int a, int b){
int pa = pathtop[a], pb = pathtop[b];
while(pathtop[a] != pathtop[b]){
if(in[pa] > in[pb]){
a = parent[pa], pa = pathtop[a];
} else{
b = parent[pb], pb = pathtop[b];
}
}
if(in[a] > in[b]) swap(a, b);
return a;
}
int dist(int a, int b){ return depth[a] + depth[b] - 2 * depth[lca(a, b)]; }
int jump(int from, int to, int k) {
if(!k) return from;
int l = lca(from, to);
int d = dist(from, to);
if(d < k) return -1;
if(depth[from] - depth[l] >= k) return la(from, k);
k -= depth[from] - depth[l];
return la(to, depth[to] - depth[l] - k);
}
void subtree_query(int a, const function<void(int, int)> &func){
func(in[a], out[a]);
}
void path_query(int a, int b, const function<void(int, int)> &func, bool include_root = true, bool reverse_path = false){
vector<pair<int, int>> path;
int pa = pathtop[a], pb = pathtop[b];
while(pathtop[a] != pathtop[b]){
if(in[pa] > in[pb]){
path.emplace_back(in[pa], in[a] + 1);
a = parent[pa], pa = pathtop[a];
} else{
path.emplace_back(in[pb], in[b] + 1);
b = parent[pb], pb = pathtop[b];
}
}
if(in[a] > in[b]) swap(a, b);
if(include_root) path.emplace_back(in[a], in[b] + 1);
else path.emplace_back(in[a] + 1, in[b] + 1);
if(!reverse_path) reverse(path.begin(), path.end());
else for(auto &p : path) p = make_pair(V - p.second, V - p.first);
for(auto [u, v] : path){
func(u, v);
}
}
void path_noncommutative_query(int a, int b, const function<void(int, int)> &func, const function<void(int, int)> &func2){
int l = lca(a, b);
path_query(a, l, func2, false, true);
path_query(l, b, func, true, false);
}
};
template <long long Modulus>
struct ModInt{
long long val;
static constexpr int mod() { return Modulus; }
constexpr ModInt(const long long _val = 0) noexcept : val(_val) {
normalize();
}
void normalize(){
val = (val % Modulus + Modulus) % Modulus;
}
inline ModInt &operator+=(const ModInt &rhs) noexcept {
if(val += rhs.val, val >= Modulus) val -= Modulus;
return *this;
}
inline ModInt &operator-=(const ModInt &rhs) noexcept {
if(val -= rhs.val, val < 0) val += Modulus;
return *this;
}
inline ModInt &operator*=(const ModInt &rhs) noexcept {
val = val * rhs.val % Modulus;
return *this;
}
inline ModInt &operator/=(const ModInt &rhs) noexcept {
val = val * inv(rhs.val).val % Modulus;
return *this;
}
inline ModInt &operator++() noexcept {
if(++val >= Modulus) val -= Modulus;
return *this;
}
inline ModInt operator++(int) noexcept {
ModInt t = val;
if(++val >= Modulus) val -= Modulus;
return t;
}
inline ModInt &operator--() noexcept {
if(--val < 0) val += Modulus;
return *this;
}
inline ModInt operator--(int) noexcept {
ModInt t = val;
if(--val < 0) val += Modulus;
return t;
}
inline ModInt operator-() const noexcept { return (Modulus - val) % Modulus; }
inline ModInt inv(void) const { return inv(val); }
ModInt pow(long long n) const {
assert(0 <= n);
ModInt x = *this, r = 1;
while(n){
if(n & 1) r *= x;
x *= x;
n >>= 1;
}
return r;
}
ModInt inv(const long long n) const {
long long a = n, b = Modulus, u = 1, v = 0;
while(b){
long long t = a / b;
a -= t * b; std::swap(a, b);
u -= t * v; std::swap(u, v);
}
u %= Modulus;
if(u < 0) u += Modulus;
return u;
}
friend inline ModInt operator+(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) += rhs; }
friend inline ModInt operator-(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) -= rhs; }
friend inline ModInt operator*(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) *= rhs; }
friend inline ModInt operator/(const ModInt &lhs, const ModInt &rhs) noexcept { return ModInt(lhs) /= rhs; }
friend inline bool operator==(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val == rhs.val; }
friend inline bool operator!=(const ModInt &lhs, const ModInt &rhs) noexcept { return lhs.val != rhs.val; }
friend inline std::istream &operator>>(std::istream &is, ModInt &x) noexcept {
is >> x.val;
x.normalize();
return is;
}
friend inline std::ostream &operator<<(std::ostream &os, const ModInt &x) noexcept { return os << x.val; }
};
#line 2 "lib/math/crt.hpp"
/**
* @brief Chinese Remainder Theorem (中国剰余定理)
* @docs docs/math/crt.md
*/
#include <numeric>
#line 10 "lib/math/crt.hpp"
namespace CRT{
inline long long mod(long long a, long long m){
return (a % m + m) % m;
}
long long extGCD(long long a, long long b, long long &x, long long &y){
if(b == 0){
x = 1;
y = 0;
return a;
}
long long d = extGCD(b, a % b, y, x);
y -= a / b * x;
return d;
}
std::pair<long long, long long> chineseRem(const std::vector<long long> &b, const std::vector<long long> &m) {
long long r = 0, M = 1;
for(int i = 0; i < (int) b.size(); i++){
long long p, q;
long long d = extGCD(M, m[i], p, q);
if((b[i] - r) % d != 0) return {0, -1};
long long tmp = (b[i] - r) / d * p % (m[i] / d);
r += M * tmp;
M *= m[i] / d;
}
r %= M;
if(r < 0) r += M;
return {r, M};
}
// not coprime
long long preGarner(std::vector<long long> &b, std::vector<long long> &m, const long long MOD){
long long res = 1;
int n = b.size();
for(int i = 0; i < n; i++){
for(int j = 0; j < i; j++){
long long g = std::gcd(m[i], m[j]);
if((b[i] - b[j]) % g != 0) return -1;
m[i] /= g, m[j] /= g;
// gcd の分だけ被ってるので振り分ける
long long gi = std::gcd(m[i], g), gj = g / gi;
do{
g = std::gcd(gi, gj);
gi *= g, gj /= g;
}while(g != 1);
m[i] *= gi, m[j] *= gj;
b[i] %= m[i], b[j] %= m[j];
}
}
for(auto x : m) (res *= x) %= MOD;
return res;
}
long long garner(const std::vector<long long> &b, const std::vector<long long> &m, const long long MOD){
std::vector<long long> tm = m;
tm.push_back(MOD);
auto inv = [&](long long a, long long m) -> long long {
long long x, y;
extGCD(a, m, x, y);
return mod(x, m);
};
int n = b.size();
std::vector<long long> coeffs(n + 1, 1), constants(n + 1, 0);
for(int i = 0; i < n; i++){
// solve "coeffs[i] * t[i] + constants[i] = b[i] (mod. m[i])
long long t = mod((b[i] - constants[i]) * inv(coeffs[i], tm[i]), tm[i]);
for(int j = i + 1; j < n + 1; j++){
(constants[j] += t * coeffs[j]) %= tm[j];
(coeffs[j] *= tm[i]) %= tm[j];
}
}
return constants[n];
}
// ax + b ≡ 0 (mod m)
long long modEquation(long long a, long long b, long long m, bool is_positive = false){
a %= m; b %= m;
b = (m - b) % m;
long long g = std::gcd(a, m);
if(b % g != 0) return -1;
a /= g; b /= g; m /= g;
if(is_positive && b == 0){
return m;
}
long long x, y;
extGCD(a, m, x, y);
return (b * x % m + m) % m;
}
}
#line 9 "lib/convolution/ntt.hpp"
#line 11 "lib/convolution/ntt.hpp"
namespace NTT{
// @param n `0 <= n`
// @return minimum non-negative `x` s.t. `n <= 2**x`
int ceil_pow2(int n) {
int x = 0;
while((1U << x) < (unsigned int) (n)) x++;
return x;
}
// @param n `1 <= n`
// @return minimum non-negative `x` s.t. `(n & (1 << x)) != 0`
int bsf(unsigned int n) {
return __builtin_ctz(n);
}
int primitive_root(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;
return 1;
}
template <typename T>
void butterfly(std::vector<T> &a){
int g = primitive_root(T::mod());
int n = int(a.size());
int h = ceil_pow2(n);
static bool first = true;
static T sum_e[30]; // sum_e[i] = ies[0] * ... * ies[i - 1] * es[i]
if(first){
first = false;
T es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(T::mod() - 1);
T e = T(g).pow((T::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;
}
T 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);
T 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))];
}
}
}
template <typename T>
void butterfly_inv(std::vector<T> &a) {
int g = primitive_root(T::mod());
int n = int(a.size());
int h = ceil_pow2(n);
static bool first = true;
static T sum_ie[30]; // sum_ie[i] = es[0] * ... * es[i - 1] * ies[i]
if(first){
first = false;
T es[30], ies[30]; // es[i]^(2^(2+i)) == 1
int cnt2 = bsf(T::mod() - 1);
T e = T(g).pow((T::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;
}
T 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);
T 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) (T::mod() + l.val - r.val) * inow.val;
}
inow *= sum_ie[bsf(~(unsigned int) (s))];
}
}
}
template <typename T>
std::vector<T> convolution(std::vector<T> a, std::vector<T> 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<T> 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 << ceil_pow2(n + m - 1);
a.resize(z);
butterfly(a);
b.resize(z);
butterfly(b);
for(int i = 0; i < z; i++){
a[i] *= b[i];
}
butterfly_inv(a);
a.resize(n + m - 1);
T iz = T(z).inv();
for(int i = 0; i < n + m - 1; i++) a[i] *= iz;
return a;
}
template <typename T>
std::vector<T> convolution_mod(const std::vector<T> &a, const std::vector<T> &b, const long long MOD){
if(MOD == 998244353){
return convolution(a, b);
}
constexpr long long M0 = 167772161;
constexpr long long M1 = 469762049;
constexpr long long M2 = 754974721;
using mint0 = ModInt<M0>;
using mint1 = ModInt<M1>;
using mint2 = ModInt<M2>;
int n = a.size(), m = b.size();
std::vector<mint0> a0(n), b0(m);
std::vector<mint1> a1(n), b1(m);
std::vector<mint2> a2(n), b2(m);
for(int i = 0; i < n; i++){
a0[i] = a[i].val;
a1[i] = a[i].val;
a2[i] = a[i].val;
}
for(int i = 0; i < m; i++){
b0[i] = b[i].val;
b1[i] = b[i].val;
b2[i] = b[i].val;
}
auto c0 = convolution(a0, b0);
auto c1 = convolution(a1, b1);
auto c2 = convolution(a2, b2);
std::vector<T> ret(n + m - 1);
for(int i = 0; i < n + m - 1; i++){
ret[i] = CRT::garner({c0[i].val, c1[i].val, c2[i].val}, {M0, M1, M2}, MOD);
}
return ret;
}
};
#line 11 "lib/polynomial/formal_power_series.hpp"
template <typename T>
struct FormalPowerSeries : std::vector<T> {
using std::vector<T>::vector;
using FPS = FormalPowerSeries;
// deg 次として初期化
FPS pre(int deg) const {
FPS res(std::begin(*this), std::begin(*this) + std::min((int) this->size(), deg));
if((int) res.size() < deg) res.resize(deg, T(0));
return res;
}
// deg 次として反転
FPS rev(int deg = -1) const {
FPS res(*this);
if(deg != -1) res.resize(deg, T(0));
std::reverse(std::begin(res), std::end(res));
return res;
}
int notZeroCount() const {
int res = 0;
for(auto x : *this){
if(x != T(0)) res++;
}
return res;
}
int maxDeg() const {
for(int i = (int) this->size() - 1; i >= 0; i--){
if((*this)[i] != T(0)) return i;
}
return -1;
}
void shrink() {
while(this->size() && this->back() == T(0)) this->pop_back();
}
std::vector<std::pair<int, T>> sparseFormat() const {
std::vector<std::pair<int, T>> res;
for(int i = 0; i < (int) this->size(); i++){
if((*this)[i] != T(0)) res.emplace_back(i, (*this)[i]);
}
return res;
}
FPS operator+(const T &rhs) const { return FPS(*this) += rhs; }
FPS operator+(const FPS &rhs) const { return FPS(*this) += rhs; }
FPS operator-(const T &rhs) const { return FPS(*this) -= rhs; }
FPS operator-(const FPS &rhs) const { return FPS(*this) -= rhs; }
FPS operator*(const T &rhs) const { return FPS(*this) *= rhs; }
FPS operator*(const FPS &rhs) const { return FPS(*this) *= rhs; }
FPS operator/(const T &rhs) const { return FPS(*this) /= rhs; }
FPS operator/(const FPS &rhs) const { return FPS(*this) /= rhs; }
FPS operator%(const FPS &rhs) const { return FPS(*this) %= rhs; }
FPS operator-() const {
FPS res(this->size());
for(int i = 0; i < (int) this->size(); i++) res[i] = -(*this)[i];
return res;
}
FPS &operator+=(const T &rhs){
if(this->empty()) this->resize(1);
(*this)[0] += rhs;
return *this;
}
FPS &operator-=(const T &rhs){
if(this->empty()) this->resize(1);
(*this)[0] -= rhs;
return *this;
}
FPS &operator*=(const T &rhs){
for(auto &x : *this) x *= rhs;
return *this;
}
FPS &operator/=(const T &rhs){
for(auto &x : *this) x /= rhs;
return *this;
}
FPS &operator+=(const FPS &rhs) noexcept {
if(this->size() < rhs.size()) this->resize(rhs.size());
for(int i = 0; i < (int) rhs.size(); i++) (*this)[i] += rhs[i];
return *this;
}
FPS &operator-=(const FPS &rhs) noexcept {
if(this->size() < rhs.size()) this->resize(rhs.size());
for(int i = 0; i < (int) rhs.size(); i++) (*this)[i] -= rhs[i];
return *this;
}
FPS &operator*=(const FPS &rhs) noexcept {
long long len1 = this->notZeroCount(), len2 = rhs.notZeroCount();
// Sparse な場合
if(len1 * len2 <= 60LL * (long long) std::max(this->size(), rhs.size())){
std::vector<std::pair<int, T>> rhs_sparse = rhs.sparseFormat();
return *this = this->multiply_naive(rhs_sparse);
}
auto res = NTT::convolution_mod(*this, rhs, T::mod());
return *this = {std::begin(res), std::end(res)};
}
// f/g = f * (g.inv())
FPS &operator/=(const FPS &rhs) noexcept {
if(this->size() < rhs.size()) return *this = FPS();
const int n = this->size() - rhs.size() + 1;
return *this = (rev().pre(n) * rhs.rev().inv(n)).pre(n).rev(n);
}
FPS &operator%=(const FPS &rhs) noexcept {
return *this -= (*this / rhs) * rhs;
}
FPS operator>>(int deg) const {
if((int) this->size() <= deg) return {};
FPS res(*this);
res.erase(std::begin(res), std::begin(res) + deg);
return res;
}
FPS operator<<(int deg) const {
FPS res(*this);
res.insert(std::begin(res), deg, T(0));
return res;
}
// 微分
FPS diff() const {
const int n = this->size();
FPS res(std::max(0, n - 1));
for(int i = 1; i < n; i++) res[i - 1] = (*this)[i] * T(i);
return res;
}
// 積分
FPS integral() const {
const int n = this->size();
FPS res(n + 1);
res[0] = T(0);
for(int i = 0; i < n; i++) res[i + 1] = (*this)[i] / T(i + 1);
return res;
}
// {lhs / rhs, lhs % rhs}
std::pair<FPS, FPS> division(const FPS &rhs) const {
FPS q = *this / rhs;
FPS r = *this - q * rhs;
q.shrink(), r.shrink();
return {q, r};
}
FPS multiply_naive(const std::vector<std::pair<int, T>> &rhs, int deg = -1){
if(deg == -1){
if(rhs.empty()) deg = this->size();
else deg = this->size() + (rhs.back().first + 1) - 1;
}
FPS res(deg, T(0));
for(auto &[i, x] : this->sparseFormat()){
for(auto &[j, y] : rhs){
if(i + j >= deg) break;
res[i + j] += x * y;
}
}
return *this = {std::begin(res), std::end(res)};
}
FPS divide_naive(const std::vector<std::pair<int, T>> &rhs){
assert(!rhs.empty());
if((int) this->size() < (rhs.back().first + 1)) return FPS();
auto [i0, x0] = rhs[0];
assert(i0 == 0 && x0 != T(0));
T x0_inv = T(1) / x0;
for(int i = 0; i < (int) this->size(); i++){
for(int i2 = 1; i2 < (int) rhs.size(); i2++){
auto &[j, y] = rhs[i2];
if(i < j) break;
(*this)[i] -= (*this)[i - j] * y;
}
(*this)[i] *= x0_inv;
}
return *this;
}
// fg = 1 (mod x^n) となる g
FPS inv(int deg = -1) const {
assert((*this)[0] != T(0));
if(deg == -1) deg = this->size();
// g_p mod x^k から g mod x^2k を求める
// (g - g_p)^2 = g^2 - 2 g g_p + (g_p)^2 = 0 (mod x^2k)
// fg^2 - 2fg g_p + f (g_p)^2
// = g - 2(g_p) + f (g_p)^2 = 0 (mod x^2k)
// g = 2(g_p) - f (g_p)^2 (mod x^2k)
FPS res({T(1) / (*this)[0]});
for(int i = 1; i < deg; i <<= 1) {
res = (res + res - res * res * pre(i << 1)).pre(i << 1);
}
return res.pre(deg);
}
// g = log f となる g
FPS log(int deg = -1) const {
assert((*this)[0] == T(1));
if(deg == -1) deg = this->size();
// log f = integral((f' / f) dx)
return (this->diff() * this->inv(deg)).pre(deg - 1).integral().pre(deg);
}
// g = exp(f) となる g
FPS exp(int deg = -1) const {
assert((*this)[0] == T(0));
if(deg == -1) deg = this->size();
// g_p mod x^k から g mod x^2k をニュートン法で求める
// log g = f (mod x^n) であるから、
// g = g_p - (log g_p - f)/(log' g_p)
// = g_p(1 - log g_p + f) (mod x^2k)
FPS res({T(1)});
for(int i = 1; i < deg; i <<= 1) {
res = (res * (-res.log(i << 1) + pre(i << 1) + T(1))).pre(i << 1);
}
return res.pre(deg);
}
// g = f^k となる g
FPS pow(long long k, int deg = -1) const {
if(deg == -1) deg = this->size();
if(k == 0){
FPS res(deg, T(0));
res[0] = T(1);
return res;
}
// f^k = exp(log f)^k = exp(k log f)
// log を計算するのに定数項が 1 である必要があるので調整する
// 最も低次の項を a x^i として、(f / (a x^i))^k を計算してから (a x^i)^k を掛ける
for(int i = 0; i < (int) this->size(); i++){
if(k * i > deg) return FPS(deg, T(0));
if((*this)[i] != T(0)){
T inv_i = T(1) / (*this)[i];
FPS res = ((((*this) * inv_i) >> i).log(deg) * k).exp(deg) * ((*this)[i].pow(k));
res = (res << (k * i)).pre(deg);
return res;
}
}
return *this;
}
long long sqrtT(const T a) const {
const long long p = T::mod();
if(a == T(0) || a == T(1)) return a.val;
if(a.pow((p - 1) / 2) != T(1)) return -1LL;
T b = 1;
while(b.pow((p - 1) / 2) == 1) b++;
// p - 1 = m 2^e
long long m = p - 1;
int e = 0;
while(m % 2 == 0) m >>= 1, e++;
// x = a^((m + 1) / 2) (mod p)
T x = a.pow((m - 1) / 2);
// y = a^{-1} x^2 (mod p)
T y = (a * x) * x;
x *= a;
T z = b.pow(m);
while(y != 1){
int j = 0;
T t = y;
while(t != 1){
t *= t;
j++;
}
z = z.pow(1LL << (e - j - 1));
x *= z;
z *= z;
y *= z;
e = j;
}
return x.val;
}
// g^2 = f となる g
FPS sqrt(int deg = -1) const {
if(this->empty()) return {};
if(deg == -1) deg = this->size();
// inv を計算するのに定数項が非零である必要があるので調整する
if((*this)[0] == T(0)){
for(int i = 1; i < (int) this->size(); i++){
if((*this)[i] == T(0)) continue;
if(i & 1) return {};
FPS res = (*this >> i).sqrt();
if(res.empty()) return {};
res = res.pre(deg - i / 2) << (i / 2);
return res;
}
FPS res(deg, T(0));
return res;
}
// g_p mod x^k から g mod x^2k をニュートン法で求める
// g^2 = f (mod x^n) であるから、
// g = g_p - ((g_p)^2 - f)/((g_p^2)')
// = g_p - ((g_p)^2 - f)/(2 g_p)
// = 1/2 * (g_p + f/g_p (mod x^2k)
long long sqrt0 = sqrtT((*this)[0]);
if(sqrt0 == -1) return {};
FPS res({T(sqrt0)});
T inv2 = T(1) / T(2);
for(int i = 1; i < deg; i <<= 1) {
res = (res + pre(i << 1) * res.inv(i << 1)) * inv2;
}
return res.pre(deg);
}
};
#line 9 "lib/polynomial/product_of_polynomial_sequence.hpp"
template <typename T>
FormalPowerSeries<T> product(const std::vector<FormalPowerSeries<T>> &f){
auto dfs = [&](auto &self, int l, int r) -> FormalPowerSeries<T> {
if(r - l == 1) return f[l];
if(r - l == 0) return {T(1)};
int mid = (l + r) / 2;
return self(self, l, mid) * self(self, mid, r);
};
return dfs(dfs, 0, (int) f.size());
}
using mint = ModInt<998244353>;
using FPS = FormalPowerSeries<mint>;
template <typename T>
struct Combination{
std::vector<T> memo, memoinv, inv;
Combination() : memo(2, T(1)), memoinv(2, T(1)), inv(2, T(1)){}
void init(const int N){
if((int) memo.size() >= N + 1){
return;
}
int prev_len = memo.size();
memo.resize(N + 1);
memoinv.resize(N + 1);
inv.resize(N + 1);
T m = -1;
long long mod = (m.val + 1LL);
for(int i = prev_len; i <= N; ++i){
memo[i] = memo[i - 1] * i;
inv[i] = mod - inv[mod % i] * (mod / i);
memoinv[i] = memoinv[i - 1] * inv[i];
}
}
inline T fact(const int n) {
init(n);
return memo[n];
}
inline T factinv(const int n) {
init(n);
return memoinv[n];
}
inline T ncr(const int n, const int r) {
if(n < r || r < 0) return 0;
init(n);
return (memo[n] * memoinv[r]) * memoinv[n - r];
}
inline T npr(const int n, const int r) {
if(n < r || r < 0) return 0;
init(n);
return memo[n] * memoinv[n - r];
}
// 重複組み合わせ
inline T nhr(const int n, const int r) {
if(n == 0 && r == 0) return 1;
return ncr(n + r - 1, r);
}
// ボールの数、一個以上必要な箱の数、制限がない箱の数 (箱区別あり)
// a = 0 の場合は重複組み合わせ
inline T choose(const int n, const int a, const int b = 0) {
if(n == 0) return !a;
return ncr(n + b - 1, a + b - 1);
}
// +1 n 個, -1 m 個, 累積和 >= 0
inline T cataran(const int n, const int m) {
return ncr(n + m, n) - ncr(n + m, n - 1);
}
// +1 n 個, -1 m 個, 累積和 > -k
inline T cataran(const int n, const int m, const int k) {
if(m < k) return ncr(n + m, n);
if(m < n + k) return ncr(n + m, n) - ncr(n + m, m - k);
return 0;
}
// +1 n 個, -1 m 個, 累積和 < +k
inline T cataran2(const int n, const int m, const int k) {
return cataran(m, n, k);
}
};
ll T;
void input(){
in(T);
}
void solve(){
ll n, s, t; in(n, s, t);
s--, t--;
vll u(n - 1), v(n - 1);
HeavyLightDecomposition hld(n);
vector<vector<P>> G(n);
map<P, ll> e;
rep(i, n - 1){
in(u[i], v[i]);
u[i]--, v[i]--;
G[u[i]].push_back({v[i], i});
G[v[i]].push_back({u[i], i});
e[{u[i], v[i]}] = i;
e[{v[i], u[i]}] = i;
hld.add_edge(u[i], v[i]);
}
hld.build();
ll v1 = -1, v2 = -1;
{
vll a = {u[s], v[s]};
vll b = {u[t], v[t]};
ll dist = INF;
rep(i, 2) rep(j, 2){
if(chmin(dist, (ll) hld.dist(a[i], b[j]))){
v1 = a[i];
v2 = b[j];
}
}
}
ll d = hld.dist(v1, v2);
vll p = {v1};
while(p.back() != v2){
ll nxt = hld.jump(p.back(), v2, 1);
p.push_back(nxt);
}
vll check(n - 1);
check[s] = check[t] = 1;
rep(i, d){
ll x = p[i], y = p[i + 1];
ll id = e[{x, y}];
check[id] = 1;
}
Combination<mint> comb;
vector<FPS> f;
for(ll x : p){
ll cnt = 0;
for(auto [y, id] : G[x]){
if(check[id]) continue;
cnt++;
}
// out(cnt);
FPS cur(cnt + 1);
rep(i, cnt + 1){
cur[i] = comb.ncr(cnt, i) * comb.fact(i);
}
f.push_back(cur);
}
FPS res = product(f);
res = res << (d + 2);
res = res.pre(n + 1);
vector<mint> ans;
rep(i, 1, n + 1) ans.push_back(res[i]);
out(ans);
}
int main(){
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout << fixed << setprecision(20);
T = 1;
// input();
while(T--) solve();
}