結果

問題 No.2413 Multiple of 99
ユーザー Ricky_ponRicky_pon
提出日時 2023-07-21 13:48:37
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 4,314 ms / 8,000 ms
コード長 6,324 bytes
コンパイル時間 176 ms
コンパイル使用メモリ 82,464 KB
実行使用メモリ 267,760 KB
最終ジャッジ日時 2024-09-21 15:50:09
合計ジャッジ時間 49,893 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge5
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 43 ms
55,168 KB
testcase_01 AC 44 ms
55,168 KB
testcase_02 AC 48 ms
60,800 KB
testcase_03 AC 43 ms
54,528 KB
testcase_04 AC 133 ms
78,100 KB
testcase_05 AC 223 ms
80,712 KB
testcase_06 AC 178 ms
78,832 KB
testcase_07 AC 4,267 ms
267,276 KB
testcase_08 AC 43 ms
54,912 KB
testcase_09 AC 4,289 ms
267,540 KB
testcase_10 AC 4,275 ms
267,412 KB
testcase_11 AC 4,262 ms
267,760 KB
testcase_12 AC 4,314 ms
267,412 KB
testcase_13 AC 4,272 ms
267,456 KB
testcase_14 AC 4,259 ms
267,536 KB
testcase_15 AC 4,262 ms
267,584 KB
testcase_16 AC 2,107 ms
236,184 KB
testcase_17 AC 1,974 ms
223,508 KB
testcase_18 AC 3,815 ms
255,472 KB
testcase_19 AC 379 ms
88,212 KB
testcase_20 AC 261 ms
81,324 KB
testcase_21 AC 367 ms
88,012 KB
testcase_22 AC 4,017 ms
260,908 KB
testcase_23 AC 563 ms
100,736 KB
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
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

    from collections import deque

    m = (n + 1) // 2
    dq = deque([[1] * 10 for _ in range(m)])
    while len(dq) >= 2:
        a = dq.popleft()
        b = dq.popleft()
        dq.append(multiply(a, b))
    h0 = dq.popleft()

    m = n // 2
    dq = deque([[1] * 10 for _ in range(m)])
    while len(dq) >= 2:
        a = dq.popleft()
        b = dq.popleft()
        dq.append(multiply(a, b))
    h1 = dq.popleft()

    ans = 0
    for d in range(11):
        f = h0[d::11]
        g = h1[d::11]

        h = multiply(f, g)
        for i in range(len(h)):
            x = i * 11 + d * 2
            if x % 9 != 0:
                continue
            ans += pow(x, k, MOD) * h[i] % MOD
            if ans >= MOD:
                ans -= MOD
    print(ans)


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