結果

問題 No.2406 Difference of Coordinate Squared
ユーザー gew1fw
提出日時 2025-06-12 20:57:11
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 3,244 bytes
コンパイル時間 197 ms
コンパイル使用メモリ 82,068 KB
実行使用メモリ 99,568 KB
最終ジャッジ日時 2025-06-12 21:00:49
合計ジャッジ時間 3,964 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge3
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 * 1 TLE * 1 -- * 53
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 # 

import sys
import math

MOD = 998244353

def main():
    N, M = map(int, sys.stdin.readline().split())
    
    max_n = N
    fact = [1] * (max_n + 1)
    for i in range(1, max_n + 1):
        fact[i] = fact[i-1] * i % MOD
    inv_fact = [1] * (max_n + 1)
    inv_fact[max_n] = pow(fact[max_n], MOD-2, MOD)
    for i in range(max_n-1, -1, -1):
        inv_fact[i] = inv_fact[i+1] * (i+1) % MOD
    
    inv_2 = pow(2, MOD-2, MOD)
    inv_2_pows = pow(inv_2, 2*N, MOD)
    
    def comb(n, k):
        if k < 0 or k > n:
            return 0
        return fact[n] * inv_fact[k] % MOD * inv_fact[n - k] % MOD
    
    def get_divisors(m):
        divisors = set()
        if m == 0:
            return divisors
        m_abs = abs(m)
        for i in range(1, int(math.isqrt(m_abs)) + 1):
            if m_abs % i == 0:
                divisors.add(i)
                divisors.add(m_abs // i)
        divisors.add(m_abs)
        res = set()
        for d in divisors:
            res.add(d)
            res.add(-d)
        return res
    
    answer = 0
    
    if M == 0:
        for a in range(N+1):
            b = N - a
            sum_x_sq = 0
            sum_y_sq = 0
            for s in range(-a, a+1, 2):
                cnt_x = comb(a, (a + s) // 2)
                if cnt_x == 0:
                    continue
                for t in [-s, s]:
                    if abs(t) > b or (b - t) % 2 != 0:
                        continue
                    cnt_y = comb(b, (b + t) // 2)
                    if cnt_y == 0:
                        continue
                    term = comb(N, a)
                    term = term * cnt_x % MOD
                    term = term * cnt_y % MOD
                    term = term * inv_2_pows % MOD
                    answer = (answer + term) % MOD
        print(answer)
        return
    
    divisors = get_divisors(M)
    required_parity = N % 2
    
    for A in divisors:
        B = M // A
        if (A % 2 != required_parity) or (B % 2 != required_parity):
            continue
        X = (A + B) // 2
        Y = (B - A) // 2
        if (A + B) % 2 != 0 or (B - A) % 2 != 0:
            continue
        
        abs_X = abs(X)
        abs_Y = abs(Y)
        min_a = abs_X
        max_a = N - abs_Y
        if min_a > max_a:
            continue
        a_parity = X % 2
        start_a = min_a if (min_a % 2 == a_parity) else (min_a + 1)
        if start_a > max_a:
            continue
        num_steps = (max_a - start_a) // 2 + 1
        
        for k in range(num_steps):
            a = start_a + 2 * k
            b_val = N - a
            if b_val < abs_Y:
                continue
            if (b_val % 2) != (Y % 2):
                continue
            
            c_n_a = comb(N, a)
            if c_n_a == 0:
                continue
            
            x = X
            y = Y
            c_a = comb(a, (a + x) // 2)
            c_b = comb(b_val, (b_val + y) // 2)
            if c_a == 0 or c_b == 0:
                continue
            
            term = c_n_a * c_a % MOD
            term = term * c_b % MOD
            term = term * inv_2_pows % MOD
            answer = (answer + term) % MOD
    
    print(answer % MOD)

if __name__ == '__main__':
    main()
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