結果

問題 No.2413 Multiple of 99
ユーザー Ricky_pon
提出日時 2023-07-21 13:01:30
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 4,204 ms / 8,000 ms
コード長 6,488 bytes
コンパイル時間 235 ms
コンパイル使用メモリ 82,432 KB
実行使用メモリ 274,292 KB
最終ジャッジ日時 2024-09-21 15:06:28
合計ジャッジ時間 49,613 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge1
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ファイルパターン 結果
sample AC * 3
other AC * 21
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ソースコード

diff #
プレゼンテーションモードにする

MOD = 998244353
IMAG = 911660635
IIMAG = 86583718
rate2 = (
    0,
    911660635,
    509520358,
    369330050,
    332049552,
    983190778,
    123842337,
    238493703,
    975955924,
    603855026,
    856644456,
    131300601,
    842657263,
    730768835,
    942482514,
    806263778,
    151565301,
    510815449,
    503497456,
    743006876,
    741047443,
    56250497,
    867605899,
    0,
)
irate2 = (
    0,
    86583718,
    372528824,
    373294451,
    645684063,
    112220581,
    692852209,
    155456985,
    797128860,
    90816748,
    860285882,
    927414960,
    354738543,
    109331171,
    293255632,
    535113200,
    308540755,
    121186627,
    608385704,
    438932459,
    359477183,
    824071951,
    103369235,
    0,
)
rate3 = (
    0,
    372528824,
    337190230,
    454590761,
    816400692,
    578227951,
    180142363,
    83780245,
    6597683,
    70046822,
    623238099,
    183021267,
    402682409,
    631680428,
    344509872,
    689220186,
    365017329,
    774342554,
    729444058,
    102986190,
    128751033,
    395565204,
    0,
)
irate3 = (
    0,
    509520358,
    929031873,
    170256584,
    839780419,
    282974284,
    395914482,
    444904435,
    72135471,
    638914820,
    66769500,
    771127074,
    985925487,
    262319669,
    262341272,
    625870173,
    768022760,
    859816005,
    914661783,
    430819711,
    272774365,
    530924681,
    0,
)
def butterfly(a):
    n = len(a)
    h = (n - 1).bit_length()
    le = 0
    while le < h:
        if h - le == 1:
            p = 1 << (h - le - 1)
            rot = 1
            for s in range(1 << le):
                offset = s << (h - le)
                for i in range(p):
                    l = a[i + offset]
                    r = a[i + offset + p] * rot
                    a[i + offset] = (l + r) % MOD
                    a[i + offset + p] = (l - r) % MOD
                rot *= rate2[(~s & -~s).bit_length()]
                rot %= MOD
            le += 1
        else:
            p = 1 << (h - le - 2)
            rot = 1
            for s in range(1 << le):
                rot2 = rot * rot % MOD
                rot3 = rot2 * rot % MOD
                offset = s << (h - le)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p] * rot
                    a2 = a[i + offset + p * 2] * rot2
                    a3 = a[i + offset + p * 3] * rot3
                    a1na3imag = (a1 - a3) % MOD * IMAG
                    a[i + offset] = (a0 + a2 + a1 + a3) % MOD
                    a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD
                    a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD
                    a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD
                rot *= rate3[(~s & -~s).bit_length()]
                rot %= MOD
            le += 2
def butterfly_inv(a):
    n = len(a)
    h = (n - 1).bit_length()
    le = h
    while le:
        if le == 1:
            p = 1 << (h - le)
            irot = 1
            for s in range(1 << (le - 1)):
                offset = s << (h - le + 1)
                for i in range(p):
                    l = a[i + offset]
                    r = a[i + offset + p]
                    a[i + offset] = (l + r) % MOD
                    a[i + offset + p] = (l - r) * irot % MOD
                irot *= irate2[(~s & -~s).bit_length()]
                irot %= MOD
            le -= 1
        else:
            p = 1 << (h - le)
            irot = 1
            for s in range(1 << (le - 2)):
                irot2 = irot * irot % MOD
                irot3 = irot2 * irot % MOD
                offset = s << (h - le + 2)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p]
                    a2 = a[i + offset + p * 2]
                    a3 = a[i + offset + p * 3]
                    a2na3iimag = (a2 - a3) * IIMAG % MOD
                    a[i + offset] = (a0 + a1 + a2 + a3) % MOD
                    a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD
                    a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD
                    a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD
                irot *= irate3[(~s & -~s).bit_length()]
                irot %= MOD
            le -= 2
def multiply(s, t):
    n = len(s)
    m = len(t)
    if min(n, m) <= 60:
        a = [0] * (n + m - 1)
        for i in range(n):
            if i % 8 == 0:
                for j in range(m):
                    a[i + j] += s[i] * t[j]
                    a[i + j] %= MOD
            else:
                for j in range(m):
                    a[i + j] += s[i] * t[j]
        return [x % MOD for x in a]
    a = s.copy()
    b = t.copy()
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    b += [0] * (z - m)
    butterfly(a)
    butterfly(b)
    for i in range(z):
        a[i] *= b[i]
        a[i] %= MOD
    butterfly_inv(a)
    a = a[: n + m - 1]
    iz = pow(z, MOD - 2, MOD)
    return [v * iz % MOD for v in a]
def main():
    n, k = map(int, input().split())
    fact = [1] * (10 * n)
    for i in range(1, len(fact)):
        fact[i] = fact[i - 1] * i % MOD
    inv_fact = [1] * (10 * n)
    inv_fact[-1] = pow(fact[-1], -1, MOD)
    for i in reversed(range(len(inv_fact) - 1)):
        inv_fact[i] = inv_fact[i + 1] * (i + 1) % MOD
    def comb(x, y):
        return fact[x] * inv_fact[y] * inv_fact[x - y] % MOD
    m = (n + 1) // 2
    f = [0] * (10 * m + 1)
    for i in range(m + 1):
        tmp = comb(m, i)
        if i % 2 == 1:
            tmp = -tmp % MOD
        f[i * 10] = tmp
    g = [0] * (9 * m + 1)
    for i in range(len(g)):
        g[i] = comb(i + m - 1, i)
    h0 = multiply(f, g)[: 9 * m + 1]
    m = n // 2
    f = [0] * (10 * m + 1)
    for i in range(m + 1):
        tmp = comb(m, i)
        if i % 2 == 1:
            tmp = -tmp % MOD
        f[i * 10] = tmp
    g = [0] * (9 * m + 1)
    for i in range(len(g)):
        g[i] = comb(i + m - 1, i)
    h1 = multiply(f, g)[: 9 * m + 1]
    ans = 0
    for d in range(11):
        f = [0] * len(h0)
        f[d::11] = h0[d::11]
        g = [0] * len(h1)
        g[d::11] = h1[d::11]
        h = multiply(f, g)
        for i in range(0, len(h), 9):
            ans += pow(i, k, MOD) * h[i] % MOD
            if ans >= MOD:
                ans -= MOD
    print(ans)
if __name__ == "__main__":
    main()
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