結果

問題 No.2406 Difference of Coordinate Squared
コンテスト
ユーザー Focus_Sash
提出日時 2023-08-05 10:57:50
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 471 ms / 2,000 ms
コード長 4,762 bytes
コンパイル時間 2,015 ms
コンパイル使用メモリ 207,372 KB
最終ジャッジ日時 2025-02-15 23:31:06
ジャッジサーバーID
（参考情報） 		judge5 / judge3
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ファイルパターン 結果
sample AC * 2
other AC * 55
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 # 

#line 1 "b.cpp"
#include "bits/stdc++.h"

using namespace std;

namespace util {
using ll = long long;
using vl = std::vector<long long>;
using pl = std::pair<long long, long long>;
}  // namespace util
using namespace util;

#include <atcoder/modint>

#line 1 "cp-library/binomial.hpp"
#include <cassert>
#include <vector>

template <typename T>
class Binomial {
 private:
  int size_, mod_;
  std::vector<T> fact_, fact_inv_, inv_;

 public:
  explicit Binomial(int size) : size_(size), mod_(T::mod()) {
    fact_.resize(size + 1);
    fact_inv_.resize(size + 1);
    inv_.resize(size + 1);
    fact_[0] = fact_[1] = 1;
    fact_inv_[0] = fact_inv_[1] = 1;
    inv_[1] = 1;
    for (int i = 2; i <= size; ++i) {
      fact_[i] = fact_[i - 1] * i;
      inv_[i] = T(mod_) - inv_[mod_ % i] * (mod_ / i);
      fact_inv_[i] = fact_inv_[i - 1] * inv_[i];
    }
  }

  T Calc(int n, int k) {
    assert(n <= size_);
    if (k < 0 || n < 0 || n < k) return 0;
    if (k == 0) {
      return 1;
    }

    return fact_[n] * fact_inv_[n - k] * fact_inv_[k];
  }

  T Factorial(int k) {
    assert(k >= 0 && k <= size_);
    return fact_[k];
  }

  T FactorialInv(int k) {
    assert(k >= 0 && k <= size_);
    return fact_inv_[k];
  }
};
#line 2 "cp-library/cutils.hpp"
#include <cmath>
constexpr long long kMax = std::numeric_limits<long long>::max();

inline long long CountDigit(long long n, const long long base = 10) {
  assert(n > 0);
  assert(base > 1);
  long long res = 0;
  while (n) {
    res++;
    n /= base;
  }
  return res;
}

// verified
inline long long Pow(long long x, long long n) {
  assert(n >= 0);
  if (x == 0) return 0;
  long long res = 1LL;
  while (n > 0) {
    if (n & 1) {
      assert(x != 0 && std::abs(res) <= kMax / std::abs(x));
      res = res * x;
    }
    if (n >>= 1) {
      assert(x != 0 && std::abs(x) <= kMax / std::abs(x));
      x = x * x;
    }
  }
  return res;
}

// verified
inline long long Mod(long long n, const long long m) {
  // returns the "arithmetic modulo"
  // for a pair of integers (n, m) with m != 0, there exists a unique pair of
  // integer (q, r) s.t. n = qm + r and 0 <= r < |m| returns this r
  assert(m != 0);
  if (m < 0) return Mod(n, -m);
  if (n >= 0)
    return n % m;
  else
    return (m + n % m) % m;
}

inline long long Quotient(long long n, long long m) {
  // returns the "arithmetic quotient"
  assert((n - Mod(n, m)) % m == 0);
  return (n - Mod(n, m)) / m;
}

inline long long DivFloor(long long n, long long m) {
  // returns floor(n / m)
  assert(m != 0);
  if (m < 0) {
    n = -n;
    m = -m;
  }
  if (n >= 0)
    return n / m;
  else if (n % m == 0)
    return -(std::abs(n) / m);
  else
    return -(std::abs(n) / m) - 1;
}

inline long long DivCeil(long long n, long long m) {
  // returns ceil(n / m)
  assert(m != 0);
  if (n % m == 0)
    return DivFloor(n, m);
  else
    return DivFloor(n, m) + 1;
}

inline long long PowMod(long long x, long long n, const long long m) {
  assert(n >= 0);
  assert(m != 0);
  if (x == 0) return 0;
  long long res = 1;
  x = Mod(x, m);
  while (n > 0) {
    if (n & 1) {
      assert(x == 0 || std::abs(res) <= kMax / std::abs(x));
      res = Mod(res * x, m);
    }
    if (n >>= 1) {
      assert(x == 0 || std::abs(x) <= kMax / std::abs(x));
      x = Mod(x * x, m);
    }
  }
  return res;
}

long long SqrtFloor(long long n) {
  // n -> floor(sqrt(n))
  assert(n >= 0);
  if (n == 0) return 0;
  long long ok = 0;
  long long ng = n + 1;
  while (ng - ok > 1) {
    long long mid = (ok + ng) / 2;
    if (mid <= n / mid) {
      ok = mid;
    } else {
      ng = mid;
    }
  }
  return ok;
}

long long SqrtCeil(long long n) {
  // n -> ceil(sqrt(n))
  assert(n >= 0);
  if (n == 0) return 0;
  long long ok = n;
  long long ng = 0;
  while (ok - ng > 1) {
    long long mid = (ok + ng) / 2;
    if (mid >= n / mid) {
      ok = mid;
    } else {
      ng = mid;
    }
  }
  return ok;
}
#line 14 "b.cpp"
using namespace atcoder;
using mint = modint998244353;

#include <unordered_map>

void solve() {
  ll n, m;
  cin >> n >> m;
  mint ans = 0;
  unordered_map<ll, ll> sq;

  for (ll i = 0; i <= n; ++i) {
    sq[i * i] = i;
  }
  Binomial<mint> binom(n + 1);

  for (ll y = -n; y <= n; ++y) {
    if (m + y * y < 0) continue;
    if (!sq.count(m + y * y)) continue;
    ll x = sq[m + y * y];
    if ((x + y + n) % 2) continue;
    ans += binom.Calc(n, (x + y + n) / 2) * binom.Calc(n, (x - y + n) / 2);
    if (x != 0) {
      ans += binom.Calc(n, (-x + y + n) / 2) * binom.Calc(n, (-x - y + n) / 2);
    }
  }
  ans *= mint(4).inv().pow(n);
  cout << ans.val() << '\n';
}

int main() {
  std::cin.tie(nullptr);
  std::ios::sync_with_stdio(false);
  std::cout << std::fixed << std::setprecision(15);

  solve();

  return 0;
}
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