結果

問題 No.2084 Mex Subset For All Sequences
ユーザー qwewe
提出日時 2025-04-24 12:20:48
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 166 ms / 2,000 ms
コード長 2,210 bytes
コンパイル時間 174 ms
コンパイル使用メモリ 82,384 KB
実行使用メモリ 91,176 KB
最終ジャッジ日時 2025-04-24 12:22:58
合計ジャッジ時間 4,016 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
このコードへのチャレンジ
（要ログイン）
ファイルパターン 結果
sample AC * 3
other AC * 25
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 # 

MOD = 998244353

def main():
    import sys
    N, M = map(int, sys.stdin.readline().split())
    if M == 0:
        print(0)
        return
    
    max_fact = M + 2
    fact = [1] * (max_fact + 1)
    for i in range(1, max_fact + 1):
        fact[i] = fact[i-1] * i % MOD
    
    inv_fact = [1] * (max_fact + 1)
    inv_fact[max_fact] = pow(fact[max_fact], MOD-2, MOD)
    for i in range(max_fact - 1, -1, -1):
        inv_fact[i] = inv_fact[i+1] * (i+1) % 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
    
    # Precompute C(M, s) for s in 0..M
    C = [0] * (M + 1)
    for s in range(0, M + 1):
        C[s] = comb(M, s)
    
    pow_M_N = pow(M, N, MOD)
    
    # Precompute (2M-1 - s)^N mod MOD for s in 0..M-1
    pow_2M_1_minus_s_N = []
    for s in range(0, M):
        base = (2 * M - 1 - s) % MOD
        pow_val = pow(base, N, MOD)
        pow_2M_1_minus_s_N.append(pow_val)
    
    # Precompute (2M - s)^N mod MOD for s in 0..M
    pow_2M_minus_s_N = []
    for s in range(0, M + 1):
        base = (2 * M - s) % MOD
        pow_val = pow(base, N, MOD)
        pow_2M_minus_s_N.append(pow_val)
    
    sum_part1 = 0
    for s in range(0, M):
        term1 = pow_2M_1_minus_s_N[s]
        term2 = pow_M_N
        diff = (term1 - term2) % MOD
        sign_mod = 1 if s % 2 == 0 else MOD - 1
        
        c1 = comb(M, s + 1)
        c2 = comb(M, s + 2)
        binomial_part = (s * c1 + (s + 1) * c2) % MOD
        
        contribution = (sign_mod * diff) % MOD
        contribution = contribution * binomial_part % MOD
        sum_part1 = (sum_part1 + contribution) % MOD
    
    sum_part2 = 0
    for s in range(0, M + 1):
        term1 = pow_2M_minus_s_N[s]
        term2 = pow_M_N
        diff = (term1 - term2) % MOD
        sign_mod = 1 if s % 2 == 0 else MOD - 1
        
        c = C[s]
        contribution = (sign_mod * c) % MOD
        contribution = contribution * diff % MOD
        contribution = contribution * M % MOD
        sum_part2 = (sum_part2 + contribution) % MOD
    
    total = (sum_part1 + sum_part2) % MOD
    print(total)

if __name__ == "__main__":
    main()
0