結果

問題 No.1067 #いろいろな色 / Red and Blue and more various colors (Middle)
ユーザー qwewe
提出日時 2025-04-24 12:32:40
言語 PyPy3
(7.3.15)
結果
WA  
実行時間 -
コード長 2,608 bytes
コンパイル時間 356 ms
コンパイル使用メモリ 82,532 KB
実行使用メモリ 360,196 KB
最終ジャッジ日時 2025-04-24 12:34:00
合計ジャッジ時間 6,440 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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 * 1
other AC * 24 WA * 1
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
    input = sys.stdin.read
    data = input().split()
    ptr = 0
    N = int(data[ptr])
    ptr += 1
    Q = int(data[ptr])
    ptr += 1
    A = list(map(int, data[ptr:ptr+N]))
    ptr += N
    A.sort()
    
    # Compute prefix products (0-based)
    prefix = [1] * (N + 1)
    for i in range(1, N + 1):
        prefix[i] = (prefix[i-1] * (A[i-1] % MOD)) % MOD
    
    # Compute suffix products (1-based)
    suffix = [1] * (N + 2)
    for i in range(N, 0, -1):
        term = (A[i-1] - 1) % MOD
        suffix[i] = (term * suffix[i+1]) % MOD
    
    # Compute x_i (modular inverses)
    x = [0] * (N + 2)  # x[1..N]
    for i in range(1, N + 1):
        a = A[i-1]
        term = (a - 1) % MOD
        if term == 0:
            x[i] = 0
        else:
            x[i] = pow(term, MOD-2, MOD)
    
    # Precompute dp table (1-based)
    dp = [[0] * (N + 2) for _ in range(N + 2)]
    for k in range(N, 0, -1):
        max_p = N - k + 1
        dp[k][0] = 1
        for p in range(1, max_p + 1):
            if k == N:
                dp[k][p] = x[k] if p == 1 else 0
            else:
                dp[k][p] = (dp[k+1][p] + x[k] * dp[k+1][p-1]) % MOD
    
    # Process queries
    output = []
    for _ in range(Q):
        l = int(data[ptr])
        ptr += 1
        r = int(data[ptr])
        ptr += 1
        p = int(data[ptr])
        ptr += 1
        xor_result = 0
        for c in range(l, r + 1):
            # Binary search for the first index >= c (0-based)
            low, high = 0, N - 1
            k = N  # if all elements are < c, then k = N (0-based)
            while low <= high:
                mid = (low + high) // 2
                if A[mid] >= c:
                    k = mid
                    high = mid - 1
                else:
                    low = mid + 1
            # k is 0-based index of first element >= c
            m = N - k
            if m < p:
                fc = 0
            else:
                product_active = suffix[k + 1]  # convert to 1-based
                if product_active == 0:
                    fc = 0
                else:
                    product_non_active = prefix[k]
                    if p > (m):
                        s_p = 0
                    else:
                        s_p = dp[k + 1][p]  # k+1 is 1-based
                    fc = (product_non_active * product_active) % MOD
                    fc = (fc * s_p) % MOD
            xor_result ^= fc
        output.append(xor_result % MOD)
    
    print('\n'.join(map(str, output)))
    
if __name__ == "__main__":
    main()
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