結果
| 問題 |
No.1482 Swap Many Permutations
|
| コンテスト | |
| ユーザー |
 tokusakurai
|
| 提出日時 | 2023-07-13 21:50:19 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 15,318 bytes |
| コンパイル時間 | 2,583 ms |
| コンパイル使用メモリ | 219,020 KB |
| 最終ジャッジ日時 | 2025-02-15 10:16:56 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 10 TLE * 1 -- * 34 |
ソースコード
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
#define per(i, n) for (int i = (n)-1; i >= 0; i--)
#define rep2(i, l, r) for (int i = (l); i < (r); i++)
#define per2(i, l, r) for (int i = (r)-1; i >= (l); i--)
#define each(e, v) for (auto &e : v)
#define MM << " " <<
#define pb push_back
#define eb emplace_back
#define all(x) begin(x), end(x)
#define rall(x) rbegin(x), rend(x)
#define sz(x) (int)x.size()
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;
template <typename T>
using minheap = priority_queue<T, vector<T>, greater<T>>;
template <typename T>
using maxheap = priority_queue<T>;
template <typename T>
bool chmax(T &x, const T &y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
bool chmin(T &x, const T &y) {
return (x > y) ? (x = y, true) : false;
}
template <typename T>
int flg(T x, int i) {
return (x >> i) & 1;
}
int pct(int x) { return __builtin_popcount(x); }
int pct(ll x) { return __builtin_popcountll(x); }
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int botbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int botbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
template <typename T>
void print(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << (i == n - 1 ? '\n' : ' ');
if (v.empty()) cout << '\n';
}
template <typename T>
void printn(const vector<T> &v, T x = 0) {
int n = v.size();
for (int i = 0; i < n; i++) cout << v[i] + x << '\n';
}
template <typename T>
int lb(const vector<T> &v, T x) {
return lower_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, T x) {
return upper_bound(begin(v), end(v), x) - begin(v);
}
template <typename T>
void rearrange(vector<T> &v) {
sort(begin(v), end(v));
v.erase(unique(begin(v), end(v)), end(v));
}
template <typename T>
vector<int> id_sort(const vector<T> &v, bool greater = false) {
int n = v.size();
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
sort(begin(ret), end(ret), [&](int i, int j) { return greater ? v[i] > v[j] : v[i] < v[j]; });
return ret;
}
template <typename T>
void reorder(vector<T> &a, const vector<int> &ord) {
int n = a.size();
vector<T> b(n);
for (int i = 0; i < n; i++) b[i] = a[ord[i]];
swap(a, b);
}
template <typename T>
T floor(T x, T y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return (x >= 0 ? x / y : (x - y + 1) / y);
}
template <typename T>
T ceil(T x, T y) {
assert(y != 0);
if (y < 0) x = -x, y = -y;
return (x >= 0 ? (x + y - 1) / y : x / y);
}
template <typename S, typename T>
pair<S, T> operator+(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first + q.first, p.second + q.second);
}
template <typename S, typename T>
pair<S, T> operator-(const pair<S, T> &p, const pair<S, T> &q) {
return make_pair(p.first - q.first, p.second - q.second);
}
template <typename S, typename T>
istream &operator>>(istream &is, pair<S, T> &p) {
S a;
T b;
is >> a >> b;
p = make_pair(a, b);
return is;
}
template <typename S, typename T>
ostream &operator<<(ostream &os, const pair<S, T> &p) {
return os << p.first << ' ' << p.second;
}
struct io_setup {
io_setup() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cout << fixed << setprecision(15);
}
} io_setup;
constexpr int inf = (1 << 30) - 1;
constexpr ll INF = (1LL << 60) - 1;
// constexpr int MOD = 1000000007;
constexpr int MOD = 998244353;
template <int mod>
struct Mod_Int {
int x;
Mod_Int() : x(0) {}
Mod_Int(long long y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
static int get_mod() { return mod; }
Mod_Int &operator+=(const Mod_Int &p) {
if ((x += p.x) >= mod) x -= mod;
return *this;
}
Mod_Int &operator-=(const Mod_Int &p) {
if ((x += mod - p.x) >= mod) x -= mod;
return *this;
}
Mod_Int &operator*=(const Mod_Int &p) {
x = (int)(1LL * x * p.x % mod);
return *this;
}
Mod_Int &operator/=(const Mod_Int &p) {
*this *= p.inverse();
return *this;
}
Mod_Int &operator++() { return *this += Mod_Int(1); }
Mod_Int operator++(int) {
Mod_Int tmp = *this;
++*this;
return tmp;
}
Mod_Int &operator--() { return *this -= Mod_Int(1); }
Mod_Int operator--(int) {
Mod_Int tmp = *this;
--*this;
return tmp;
}
Mod_Int operator-() const { return Mod_Int(-x); }
Mod_Int operator+(const Mod_Int &p) const { return Mod_Int(*this) += p; }
Mod_Int operator-(const Mod_Int &p) const { return Mod_Int(*this) -= p; }
Mod_Int operator*(const Mod_Int &p) const { return Mod_Int(*this) *= p; }
Mod_Int operator/(const Mod_Int &p) const { return Mod_Int(*this) /= p; }
bool operator==(const Mod_Int &p) const { return x == p.x; }
bool operator!=(const Mod_Int &p) const { return x != p.x; }
Mod_Int inverse() const {
assert(*this != Mod_Int(0));
return pow(mod - 2);
}
Mod_Int pow(long long k) const {
Mod_Int now = *this, ret = 1;
for (; k > 0; k >>= 1, now *= now) {
if (k & 1) ret *= now;
}
return ret;
}
friend ostream &operator<<(ostream &os, const Mod_Int &p) { return os << p.x; }
friend istream &operator>>(istream &is, Mod_Int &p) {
long long a;
is >> a;
p = Mod_Int<mod>(a);
return is;
}
};
using mint = Mod_Int<MOD>;
template <typename T>
struct Combination {
static vector<T> _fac, _ifac;
Combination() {}
static void init(int n) {
_fac.resize(n + 1), _ifac.resize(n + 1);
_fac[0] = 1;
for (int i = 1; i <= n; i++) _fac[i] = _fac[i - 1] * i;
_ifac[n] = _fac[n].inverse();
for (int i = n; i >= 1; i--) _ifac[i - 1] = _ifac[i] * i;
}
static T fac(int k) { return _fac[k]; }
static T ifac(int k) { return _ifac[k]; }
static T inv(int k) { return fac(k - 1) * ifac(k); }
static T P(int n, int k) {
if (k < 0 || n < k) return 0;
return fac(n) * ifac(n - k);
}
static T C(int n, int k) {
if (k < 0 || n < k) return 0;
return fac(n) * ifac(n - k) * ifac(k);
}
// n 個の区別できる箱に、k 個の区別できない玉を入れる場合の数
static T H(int n, int k) {
if (n < 0 || k < 0) return 0;
return k == 0 ? 1 : C(n + k - 1, k);
}
// n 個の区別できる玉を、k 個の区別しない箱に、各箱に 1 個以上玉が入るように入れる場合の数
static T second_stirling_number(int n, int k) {
T ret = 0;
for (int i = 0; i <= k; i++) {
T tmp = C(k, i) * T(i).pow(n);
ret += ((k - i) & 1) ? -tmp : tmp;
}
return ret * ifac(k);
}
// n 個の区別できる玉を、k 個の区別しない箱に入れる場合の数
static T bell_number(int n, int k) {
if (n == 0) return 1;
k = min(k, n);
vector<T> pref(k + 1);
pref[0] = 1;
for (int i = 1; i <= k; i++) {
if (i & 1) {
pref[i] = pref[i - 1] - ifac(i);
} else {
pref[i] = pref[i - 1] + ifac(i);
}
}
T ret = 0;
for (int i = 1; i <= k; i++) ret += T(i).pow(n) * ifac(i) * pref[k - i];
return ret;
}
};
template <typename T>
vector<T> Combination<T>::_fac = vector<T>();
template <typename T>
vector<T> Combination<T>::_ifac = vector<T>();
using comb = Combination<mint>;
template <typename T>
struct Number_Theoretic_Transform {
static int max_base;
static T root;
static vector<T> r, ir;
Number_Theoretic_Transform() {}
static void init() {
if (!r.empty()) return;
int mod = T::get_mod();
int tmp = mod - 1;
root = 2;
while (root.pow(tmp >> 1) == 1) root++;
max_base = 0;
while (tmp % 2 == 0) tmp >>= 1, max_base++;
r.resize(max_base), ir.resize(max_base);
for (int i = 0; i < max_base; i++) {
r[i] = -root.pow((mod - 1) >> (i + 2)); // r[i] := 1 の 2^(i+2) 乗根
ir[i] = r[i].inverse(); // ir[i] := 1/r[i]
}
}
static void ntt(vector<T> &a) {
init();
int n = a.size();
assert((n & (n - 1)) == 0);
assert(n <= (1 << max_base));
for (int k = n; k >>= 1;) {
T w = 1;
for (int s = 0, t = 0; s < n; s += 2 * k) {
for (int i = s, j = s + k; i < s + k; i++, j++) {
T x = a[i], y = w * a[j];
a[i] = x + y, a[j] = x - y;
}
w *= r[__builtin_ctz(++t)];
}
}
}
static void intt(vector<T> &a) {
init();
int n = a.size();
assert((n & (n - 1)) == 0);
assert(n <= (1 << max_base));
for (int k = 1; k < n; k <<= 1) {
T w = 1;
for (int s = 0, t = 0; s < n; s += 2 * k) {
for (int i = s, j = s + k; i < s + k; i++, j++) {
T x = a[i], y = a[j];
a[i] = x + y, a[j] = w * (x - y);
}
w *= ir[__builtin_ctz(++t)];
}
}
T inv = T(n).inverse();
for (auto &e : a) e *= inv;
}
static vector<T> convolve(vector<T> a, vector<T> b) {
if (a.empty() || b.empty()) return {};
if (min(a.size(), b.size()) < 40) {
int n = a.size(), m = b.size();
vector<T> c(n + m - 1, 0);
for (int i = 0; i < n; i++) {
for (int j = 0; j < m; j++) c[i + j] += a[i] * b[j];
}
return c;
}
int k = (int)a.size() + (int)b.size() - 1, n = 1;
while (n < k) n <<= 1;
a.resize(n, 0), b.resize(n, 0);
ntt(a), ntt(b);
for (int i = 0; i < n; i++) a[i] *= b[i];
intt(a), a.resize(k);
return a;
}
};
template <typename T>
int Number_Theoretic_Transform<T>::max_base = 0;
template <typename T>
T Number_Theoretic_Transform<T>::root = T();
template <typename T>
vector<T> Number_Theoretic_Transform<T>::r = vector<T>();
template <typename T>
vector<T> Number_Theoretic_Transform<T>::ir = vector<T>();
using NTT = Number_Theoretic_Transform<mint>;
template <typename T>
struct Binary_Indexed_Tree {
vector<T> bit;
const int n;
Binary_Indexed_Tree(const vector<T> &v) : n((int)v.size()) {
bit.resize(n + 1);
copy(begin(v), end(v), begin(bit) + 1);
build();
}
Binary_Indexed_Tree(int n, T x = 0) : Binary_Indexed_Tree(vector<T>(n, x)) {}
void set(int i, const T &x) { bit[i + 1] = x; }
void build() {
for (int a = 2; a <= n; a <<= 1) {
for (int b = a; b <= n; b += a) bit[b] += bit[b - a / 2];
}
}
void add(int i, const T &x) {
for (i++; i <= n; i += (i & -i)) bit[i] += x;
}
void change(int i, const T &x) { add(i, x - query(i, i + 1)); }
T sum(int i) const {
i = min(i, n);
if (i <= 0) return 0;
T ret = 0;
for (; i > 0; i -= (i & -i)) ret += bit[i];
return ret;
}
T query(int l, int r) const {
l = max(l, 0), r = min(r, n);
if (l >= r) return 0;
return sum(r) - sum(l);
}
T operator[](int i) const { return query(i, i + 1); }
// v[0]+...+v[r] >= x を満たす最小の r (なければ n)
int lower_bound(T x) const {
int ret = 0;
for (int k = 31 - __builtin_clz(n); k >= 0; k--) {
if (ret + (1 << k) <= n && bit[ret + (1 << k)] < x) x -= bit[ret += (1 << k)];
}
return ret;
}
// v[0]+...+v[r] > x を満たす最小の r (なければ n)
int upper_bound(T x) const {
int ret = 0;
for (int k = 31 - __builtin_clz(n); k >= 0; k--) {
if (ret + (1 << k) <= n && bit[ret + (1 << k)] <= x) x -= bit[ret += (1 << k)];
}
return ret;
}
};
template <typename T>
long long inversion_number(const vector<T> &a) {
int n = a.size();
vector<int> v(n);
iota(begin(v), end(v), 0);
sort(begin(v), end(v), [&](int i, int j) {
if (a[i] != a[j]) return a[i] < a[j];
return i < j;
});
Binary_Indexed_Tree<int> bit(n, 0);
long long ret = 0;
for (int i = 0; i < n; i++) {
ret += bit.query(v[i] + 1, n);
bit.add(v[i], 1);
}
return ret;
}
// a を b に変換するのに必要な最小バブルソート回数
template <typename T>
long long inversion_number(const vector<T> &a, const vector<T> &b) {
int n = a.size();
assert(b.size() == n);
vector<int> u(n), v(n);
iota(begin(u), end(u), 0);
sort(begin(u), end(u), [&](int i, int j) {
if (a[i] != a[j]) return a[i] < a[j];
return i < j;
});
iota(begin(v), end(v), 0);
sort(begin(v), end(v), [&](int i, int j) {
if (b[i] != b[j]) return b[i] < b[j];
return i < j;
});
vector<int> w(n);
for (int i = 0; i < n; i++) {
if (a[u[i]] != b[v[i]]) return -1;
w[v[i]] = u[i];
}
Binary_Indexed_Tree<int> bit(n, 0);
long long ret = 0;
for (int i = 0; i < n; i++) {
ret += bit.query(w[i] + 1, n);
bit.add(w[i], 1);
}
return ret;
}
void solve() {
int N, M;
cin >> N >> M;
comb::init(N);
vector<int> b(N), c(N);
rep(i, N) cin >> b[i] >> c[i];
vector<int> sgn(N);
rep(i, N) {
vector<int> a(M);
rep(j, M) {
a[j] = (b[i] + c[i] * j) % M; //
}
sgn[i] = inversion_number(a) & 1;
}
vector<mint> ans(N + 1, 0);
ans[1] = 1;
if (b[0] != b[1] || c[0] != c[1]) ans[2] = M * (M - 1);
int X = 0, Y = 0;
if (M == 2) {
X = 1, Y = 1;
} else {
rep2(i, 1, M) {
vector<int> a(M);
rep(j, M) {
a[j] = i * j % M; //
}
(inversion_number(a) & 1 ? X : Y) += M;
}
}
vector<vector<mint>> x(2, vector<mint>(N + 1, 0)), y(2, vector<mint>(N + 1, 0));
{
mint t = 1;
rep(i, N + 1) {
x[i & 1][i] += t;
t *= X - i;
t /= i + 1;
}
}
{
mint t = 1;
rep(i, N + 1) {
y[i & 1][i] += t;
t *= Y - i;
t /= i + 1;
}
}
vector<vector<mint>> f(4);
rep(i, 2) rep(j, 2) f[2 * i + j] = NTT::convolve(x[i], y[j]);
int cnt = 0;
rep(i, N) {
cnt ^= sgn[i];
if (i >= 2) {
if (cnt) {
ans[i + 1] += f[2][i + 1] + f[3][i + 1];
} else {
ans[i + 1] += f[0][i + 1] + f[1][i + 1];
}
ans[i + 1] *= comb::fac(i + 1);
}
}
rep2(i, 1, N + 1) cout << ans[i] << '\n';
}
int main() {
int T = 1;
// cin >> T;
while (T--) solve();
}