結果

問題 No.1307 Rotate and Accumulate
コンテスト
ユーザー tamato
提出日時 2021-08-13 14:11:19
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 260 ms / 5,000 ms
コード長 3,119 bytes
コンパイル時間 260 ms
コンパイル使用メモリ 82,596 KB
実行使用メモリ 118,128 KB
最終ジャッジ日時 2024-10-03 04:32:46
合計ジャッジ時間 5,211 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
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 * 3
other AC * 19
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
W = (
1, 998244352, 911660635, 372528824, 929031873, 452798380, 922799308, 781712469, 476477967, 166035806, 258648936,
584193783, 63912897, 350007156, 666702199, 968855178, 629671588, 24514907, 996173970, 363395222, 565042129,
733596141, 267099868, 15311432)
IW = (1, 998244352, 86583718, 509520358, 337190230, 87557064, 609441965, 135236158, 304459705, 685443576, 381598368,
      335559352, 129292727, 358024708, 814576206, 708402881, 283043518, 3707709, 121392023, 704923114, 950391366,
      428961804, 382752275, 469870224)


def main():
    import sys
    input = sys.stdin.readline


    # A: 係数を並べたベクトル，len(A) = 2^n
    def fft(A):
        N = len(A)
        n = N.bit_length() - 1
        N2 = N // 2
        A_new = [0] * N
        for lv in range(n):
            L = 1 << (n - lv - 1)
            w = W[lv + 1]
            ww = 1
            for j in range(1 << lv):
                for i in range(L):
                    f0_val = A[i + j * L * 2]
                    f1_val = A[i + j * L * 2 + L]
                    tmp = (ww * f1_val) % mod
                    A_new[i + j * L] = (f0_val + tmp) % mod
                    A_new[i + j * L + N2] = (f0_val - tmp) % mod
                ww = (ww * w) % mod
            A, A_new = A_new, A
        return A

    # A: 係数を並べたベクトル，len(A) = 2^n
    def ifft(A):
        N = len(A)
        n = N.bit_length() - 1
        N2 = N // 2
        A_new = [0] * N
        for lv in range(n):
            L = 1 << (n - lv - 1)
            w = IW[lv + 1]
            ww = 1
            for j in range(1 << lv):
                for i in range(L):
                    f0_val = A[i + j * L * 2]
                    f1_val = A[i + j * L * 2 + L]
                    tmp = (ww * f1_val) % mod
                    A_new[i + j * L] = (f0_val + tmp) % mod
                    A_new[i + j * L + N2] = (f0_val - tmp) % mod
                ww = (ww * w) % mod
            A, A_new = A_new, A
        return A

    def convolution(A0, B0, limit):
        if len(A0) <= 60 or len(B0) <= 60:
            return convolution_naive(A0, B0, limit)
        N = len(A0) + len(B0) - 1
        N0 = 1 << ((N - 1).bit_length())
        A = A0 + [0] * (N0 - len(A0))
        B = B0 + [0] * (N0 - len(B0))
        AA = fft(A)
        BB = fft(B)
        CC = [(aa * bb) % mod for aa, bb in zip(AA, BB)]
        C = ifft(CC)
        invN0 = pow(N0, mod - 2, mod)
        C = [(c * invN0) % mod for c in C]
        return C[:limit]

    def convolution_naive(A0, B0, limit):
        NA = len(A0)
        NB = len(B0)
        C = [0] * (NA + NB - 1)
        for i in range(NA):
            for j in range(NB):
                C[i + j] = (C[i + j] + (A0[i] * B0[j]) % mod) % mod
        return C[:limit]

    N, Q = map(int, input().split())
    A = list(map(int, input().split()))
    R = list(map(int, input().split()))

    B = [0] * (N+1)
    for r in R:
        B[N-r] += 1
    C = convolution(A, B, N*2)
    ans = [0] * N
    for i in range(N):
        ans[i] = (C[i] + C[i+N])%mod
    print(*ans)


if __name__ == '__main__':
    main()
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