結果

問題 No.2474 Empty Quartz
ユーザー 👑 tute7627
提出日時 2023-09-02 11:30:23
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 231 ms / 2,000 ms
コード長 3,962 bytes
コンパイル時間 2,160 ms
コンパイル使用メモリ 199,544 KB
最終ジャッジ日時 2025-02-16 18:00:38
ジャッジサーバーID
（参考情報） 		judge4 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 5
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include<bits/stdc++.h>
using namespace std;
using ll = long long;
const int MOD9 = 998244353;
template< int mod >
struct ModInt {
  int x;
  ModInt() : x(0) {}
  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}
  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }
  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }
  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }
  ModInt operator-() const { return ModInt(-x); }
  friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) += rhs;
  }
  friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) -= rhs;
  }
  friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) *= rhs;
  }
  friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {
        return ModInt(lhs) /= rhs;
  }
  bool operator==(const ModInt &p) const { return x == p.x; }
  bool operator!=(const ModInt &p) const { return x != p.x; }
  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }
  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }
  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }
  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }
  static int get_mod() { return mod; }
};
template< typename T >
struct Combination {
  vector< T > _fact, _rfact, _inv;
  Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {
    _fact[0] = _rfact[sz] = _inv[0] = 1;
    for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;
    _rfact[sz] /= _fact[sz];
    for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);
    for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];
  }
  inline T fact(ll k) const { return _fact[k]; }
  inline T rfact(ll k) const { return _rfact[k]; }
  inline T inv(ll k) const { return _inv[k]; }
  T P(ll n, ll r) const {
    if(r < 0 || n < r) return 0;
    return fact(n) * rfact(n - r);
  }
  T C(ll p, ll q) const {
    if(q < 0 || p < q) return 0;
    return fact(p) * rfact(q) * rfact(p - q);
  }
  
  T RC(ll p, ll q) const {
    if(q < 0 || p < q) return 0;
    return rfact(p) * fact(q) * fact(p - q);
  }
  T H(ll n, ll r) const {
    if(n < 0 || r < 0) return (0);
    return r == 0 ? 1 : C(n + r - 1, r);
  }
  //+1がm個、-1がn個で prefix sumが常にk以上
  T catalan(ll m,ll n,ll k){
    if(n>m-k)return 0;
    else return C(n+m,m)-C(n+m,n+k-1);
  }
};
using modint = ModInt< MOD9 >;modint mpow(ll n, ll x){return modint(n).pow(x);}modint mpow(modint n, ll x){return n.pow(x);}
//using modint=ld;modint mpow(ll n, ll x){return pow(n,x);}modint mpow(modint n, ll x){return pow(n,x);}
using Comb=Combination<modint>;
int main(){
  int T;
  cin >> T;
  assert(1 <= T && T <= 1e5);
  Comb comb(300005);
  while(T--){
    long long N, K;
    cin >> N >> K;
    assert(1 <= N && N <= 1e5);
    assert(0 <= K && K <= N * (N + 1) / 2);
    long long d = (N + 1) * (N + 1) - 4 * K;
    if(d < 0){
      cout << 0 << endl;
      continue;
    }
    long long sq = sqrtl(d);
    if(sq * sq != d || sq % 2 != (N + 1) % 2){
      cout << 0 << endl;
      continue;
    }
    long long x = (N + 1 + sq) / 2;
    modint ret = 0;
    if(0 <= x && x <= N + 1){
      modint ret = comb.C(N, x - 1);
      if(x != N + 1 - x) ret += comb.C(N, N - x);
      cout << ret << endl;
    }
    else{
      cout << 0 << endl;
    }
  }
}
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