結果

問題 No.1474 かさまＪ
ユーザー lam6er
提出日時 2025-03-26 15:55:47
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 804 ms / 2,500 ms
コード長 2,784 bytes
コンパイル時間 383 ms
コンパイル使用メモリ 81,976 KB
実行使用メモリ 278,772 KB
最終ジャッジ日時 2025-03-26 15:56:38
合計ジャッジ時間 6,351 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
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ファイルパターン 結果
sample AC * 4
other AC * 17
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

MOD = 10**9 + 7
def main():
    import sys
    input = sys.stdin.read().split()
    idx = 0
    N = int(input[idx]); idx +=1
    M_P = int(input[idx]); idx +=1
    M_q = int(input[idx]); idx +=1
    L = int(input[idx]); idx +=1
    S = list(map(int, input[idx:idx+N]))
    idx += N
    
    # Precompute factorial and inverse factorial for combinations
    max_n = M_P + N - 1
    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
    
    def comb(n, k):
        if n < 0 or k < 0 or n < k:
            return 0
        return fact[n] * inv_fact[k] % MOD * inv_fact[n -k] % MOD
    
    # Initialize DP
    dp_current = [ [0]*(M_q +1) for _ in range(N+1) ]
    dp_current[0][0] = 1
    
    for i in range(N):
        s_i = S[i]
        dp_next = [ [0]*(M_q +1) for _ in range(N+1) ]
        diff = [ [0]*(M_q +2) for _ in range(N+2) ]  # diff[k][sum_q]
        
        for k_prev in range(N+1):
            for sum_q_prev in range(M_q +1):
                val = dp_current[k_prev][sum_q_prev]
                if val == 0:
                    continue
                # Case 1: q_i = 0
                dp_next[k_prev][sum_q_prev] = (dp_next[k_prev][sum_q_prev] + val) % MOD
                
                # Case 2: q_i >=1
                k_next = k_prev + 1
                if k_next > N:
                    continue
                # Compute start and end for sum_q_next
                lower = L * k_next - M_P
                start = max(sum_q_prev + 1, lower)
                end = min(sum_q_prev + s_i, M_q)
                if start > end:
                    continue
                # Update diff array
                diff[k_next][start] = (diff[k_next][start] + val) % MOD
                if end +1 <= M_q:
                    diff[k_next][end +1] = (diff[k_next][end +1] - val) % MOD
        
        # Apply diff to dp_next
        for k_next in range(N+1):
            current = 0
            for sum_q in range(M_q +1):
                current = (current + diff[k_next][sum_q]) % MOD
                dp_next[k_next][sum_q] = (dp_next[k_next][sum_q] + current) % MOD
        
        dp_current = dp_next
    
    # Calculate the answer
    ans = 0
    for k in range(N+1):
        for sum_q in range(M_q +1):
            if sum_q > M_q:
                continue
            sum_a = L * k - sum_q
            if sum_a < 0 or sum_a > M_P:
                continue
            rem = M_P - sum_a
            c = comb(rem + N -1, N-1)
            ans = (ans + dp_current[k][sum_q] * c) % MOD
    print(ans % MOD)
if __name__ == '__main__':
    main()
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