結果
| 問題 |
No.2512 Mountain Sequences
|
| コンテスト | |
| ユーザー |
 torisasami4
|
| 提出日時 | 2023-10-21 01:02:47 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 11,622 bytes |
| コンパイル時間 | 4,579 ms |
| コンパイル使用メモリ | 251,112 KB |
| 最終ジャッジ日時 | 2025-02-17 12:01:13 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 12 TLE * 16 -- * 1 |
ソースコード
// #define _GLIBCXX_DEBUG
#pragma GCC optimize("O2,no-stack-protector,unroll-loops,fast-math")
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < int(n); i++)
#define per(i, n) for (int i = (n)-1; 0 <= i; i--)
#define rep2(i, l, r) for (int i = (l); i < int(r); i++)
#define per2(i, l, r) for (int i = (r)-1; int(l) <= i; 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()
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';
}
using ll = long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
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 <class T>
using minheap = std::priority_queue<T, std::vector<T>, std::greater<T>>;
template <class T> using maxheap = std::priority_queue<T>;
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));
}
// __int128_t gcd(__int128_t a, __int128_t b) {
// if (a == 0)
// return b;
// if (b == 0)
// return a;
// __int128_t cnt = a % b;
// while (cnt != 0) {
// a = b;
// b = cnt;
// cnt = a % b;
// }
// return b;
// }
struct Union_Find_Tree {
vector<int> data;
const int n;
int cnt;
Union_Find_Tree(int n) : data(n, -1), n(n), cnt(n) {}
int root(int x) {
if (data[x] < 0) return x;
return data[x] = root(data[x]);
}
int operator[](int i) { return root(i); }
bool unite(int x, int y) {
x = root(x), y = root(y);
if (x == y) return false;
if (data[x] > data[y]) swap(x, y);
data[x] += data[y], data[y] = x;
cnt--;
return true;
}
int size(int x) { return -data[root(x)]; }
int count() { return cnt; };
bool same(int x, int y) { return root(x) == root(y); }
void clear() {
cnt = n;
fill(begin(data), end(data), -1);
}
};
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;
}
};
ll mpow2(ll x, ll n, ll mod) {
ll ans = 1;
x %= mod;
while (n != 0) {
if (n & 1) ans = ans * x % mod;
x = x * x % mod;
n = n >> 1;
}
ans %= mod;
return ans;
}
template <typename T> T modinv(T a, const T& m) {
T b = m, u = 1, v = 0;
while (b > 0) {
T t = a / b;
swap(a -= t * b, b);
swap(u -= t * v, v);
}
return u >= 0 ? u % m : (m - (-u) % m) % m;
}
ll divide_int(ll a, ll b) {
if (b < 0) a = -a, b = -b;
return (a >= 0 ? a / b : (a - b + 1) / b);
}
// const int MOD = 1000000007;
const int MOD = 998244353;
using mint = Mod_Int<MOD>;
// ----- library -------
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), b.resize(n);
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>();
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>();
// ----- library -------
int main() {
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout << fixed << setprecision(15);
using comb = Combination<mint>;
comb::init(5e5);
Number_Theoretic_Transform<mint> ntt;
int b = 2000;
vector<vector<mint>> f(b + 1, vector<mint>(b * 2 + 1, 0)), g(b + 1, vector<mint>(b * 2 + 1, 0));
f[0][0] = 1, g[0][0] = 1;
rep(i, b) {
f[i + 1] = f[i], g[i + 1] = g[i];
rep(j, b * 2) f[i + 1][j + 1] += f[i][j] * 2;
rep(j, b * 2 - 1) f[i + 1][j + 2] += f[i][j];
rep(j, b * 2 + 1) g[i + 1][j] += f[i + 1][j];
}
int q;
cin >> q;
vector<int> n(q), m(q);
rep(i, q) cin >> n[i] >> m[i], n[i]--, m[i]--;
vector<pii> v;
rep(i, q) v.eb(m[i], i);
sort(all(v));
const int si = 2e5;
vector<mint> dp1(1, 1), dp2(1, 0);
int idx = 0;
vector<mint> ans(q, 0);
int p = 2 * b;
for (int t = 0; t < si; t += b, p += 2 * b) {
while (idx < q && v[idx].first < t + b) {
int id = v[idx].second;
idx++;
int r = m[id] % b;
if (n[id] < sz(dp2))
ans[id] = dp2[n[id]];
rep2(i, max(0, n[id] - r * 2), min(sz(dp1), n[id] + 1)) ans[id] += dp1[i] * g[r][n[id] - i];
}
dp1.resize(min(si, p + 1));
rep(i, sz(dp1)) dp1[i] = comb::C(p, i);
dp2 = ntt.convolve(dp2, f[b]);
rep(j, b * 2 - 1) dp2[j] += g[b - 1][j];
if (sz(dp2) > si)
dp2.resize(si);
}
rep(i, q) cout << ans[i] << endl;
}