結果

問題 No.1856 Mex Sum 2
ユーザー MitarushiMitarushi
提出日時 2022-02-24 23:31:28
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,334 ms / 3,000 ms
コード長 2,041 bytes
コンパイル時間 272 ms
コンパイル使用メモリ 86,820 KB
実行使用メモリ 78,672 KB
最終ジャッジ日時 2023-09-15 10:28:32
合計ジャッジ時間 41,315 ms
ジャッジサーバーID
（参考情報） 		judge12 / judge11
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 73 ms
71,076 KB
testcase_01 AC 74 ms
70,864 KB
testcase_02 AC 104 ms
76,984 KB
testcase_03 AC 73 ms
71,076 KB
testcase_04 AC 91 ms
76,296 KB
testcase_05 AC 92 ms
76,316 KB
testcase_06 AC 90 ms
76,200 KB
testcase_07 AC 101 ms
77,212 KB
testcase_08 AC 76 ms
71,124 KB
testcase_09 AC 87 ms
76,068 KB
testcase_10 AC 89 ms
76,168 KB
testcase_11 AC 90 ms
76,184 KB
testcase_12 AC 80 ms
75,848 KB
testcase_13 AC 73 ms
70,980 KB
testcase_14 AC 77 ms
71,204 KB
testcase_15 AC 75 ms
70,976 KB
testcase_16 AC 90 ms
76,036 KB
testcase_17 AC 103 ms
77,092 KB
testcase_18 AC 102 ms
77,072 KB
testcase_19 AC 91 ms
76,336 KB
testcase_20 AC 89 ms
76,356 KB
testcase_21 AC 75 ms
71,204 KB
testcase_22 AC 103 ms
77,124 KB
testcase_23 AC 75 ms
71,080 KB
testcase_24 AC 98 ms
76,988 KB
testcase_25 AC 102 ms
77,316 KB
testcase_26 AC 73 ms
70,840 KB
testcase_27 AC 72 ms
70,840 KB
testcase_28 AC 75 ms
71,088 KB
testcase_29 AC 414 ms
78,488 KB
testcase_30 AC 278 ms
78,444 KB
testcase_31 AC 393 ms
78,064 KB
testcase_32 AC 551 ms
78,280 KB
testcase_33 AC 570 ms
78,336 KB
testcase_34 AC 400 ms
78,348 KB
testcase_35 AC 296 ms
78,568 KB
testcase_36 AC 197 ms
78,136 KB
testcase_37 AC 385 ms
78,368 KB
testcase_38 AC 176 ms
77,928 KB
testcase_39 AC 127 ms
78,044 KB
testcase_40 AC 131 ms
77,916 KB
testcase_41 AC 132 ms
77,904 KB
testcase_42 AC 1,290 ms
78,376 KB
testcase_43 AC 1,165 ms
78,360 KB
testcase_44 AC 1,224 ms
78,368 KB
testcase_45 AC 1,278 ms
78,520 KB
testcase_46 AC 1,172 ms
78,396 KB
testcase_47 AC 1,230 ms
78,400 KB
testcase_48 AC 1,298 ms
78,164 KB
testcase_49 AC 1,292 ms
78,492 KB
testcase_50 AC 1,078 ms
78,352 KB
testcase_51 AC 1,321 ms
78,492 KB
testcase_52 AC 1,323 ms
78,440 KB
testcase_53 AC 1,329 ms
78,536 KB
testcase_54 AC 1,328 ms
78,500 KB
testcase_55 AC 1,330 ms
78,372 KB
testcase_56 AC 1,328 ms
78,608 KB
testcase_57 AC 1,333 ms
78,496 KB
testcase_58 AC 1,334 ms
78,528 KB
testcase_59 AC 1,328 ms
78,672 KB
testcase_60 AC 1,328 ms
78,604 KB
testcase_61 AC 1,332 ms
78,448 KB
testcase_62 AC 1,330 ms
78,360 KB
testcase_63 AC 1,331 ms
78,368 KB
testcase_64 AC 1,331 ms
78,496 KB
testcase_65 AC 1,329 ms
78,496 KB
testcase_66 AC 1,332 ms
78,412 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 # 

def fft_inplace(a, w):
    n = len(a)
    m = n
    t = 1
    while m >= 2:
        mh = m >> 1
        for i in range(0, n, m):
            for s in range(mh):
                j, k = i+s, i+mh+s
                a[j], u = a[j]+a[k], a[j]-a[k]
                a[k] = u * w[s*t] % 998244353
        m = mh
        t *= 2


def ifft_inplace(a, w):
    n = len(a)
    m = 2
    t = -(n >> 1)
    while m <= n:
        mh = m >> 1
        for i in range(0, n, m):
            for s in range(mh):
                j, k = i+s, i+mh+s
                u = a[k] * w[s*t] % 998244353
                a[j], a[k] = a[j]+u, a[j]-u
        m <<= 1
        t //= 2
    n_inv = pow(n, 998244353-2, 998244353)
    for i in range(n):
        a[i] = a[i] * n_inv % 998244353


n, m = map(int, input().split())
assert 1 <= n <= 2000
assert 1 <= m <= 10 ** 9
fixed_n = 1 << ((n+1)*2).bit_length()

w_root = pow(3, (998244353-1)//fixed_n, 998244353)
w = [1] * fixed_n
for i in range(1, fixed_n):
    w[i] = w[i-1] * w_root % 998244353

frac = [1] * (n + 1)
for i in range(1, n+1):
    frac[i] = frac[i-1] * i % 998244353
frac_inv = [0] * (n+1)
frac_inv[n] = pow(frac[n], 998244353-2, 998244353)
for i in range(1, n+1)[::-1]:
    frac_inv[i-1] = frac_inv[i] * i % 998244353

dp1 = [0] * fixed_n
dp1[0] = 1

t = [0] * fixed_n
for i in range(n+1):
    t[i] = (pow(2, i, 998244353)-1) * pow(pow(2, i, 998244353) * frac[i], 998244353-2, 998244353) % 998244353

fft_inplace(t, w)

ans_sub = [0] * (n+1)
for k in range(min(n, m+1)):
    fft_inplace(dp1, w)
    for i, j in enumerate(t):
        dp1[i] = dp1[i] * j % 998244353
    ifft_inplace(dp1, w)

    pow_tmp = 1
    for i in range(k+1, n+1)[::-1]:
        ans_sub[i] += dp1[i] * pow_tmp % 998244353
        pow_tmp = pow_tmp * (m - k) % 998244353
    for i in range(n+1, fixed_n):
        dp1[i] = 0

ans = sum(ans_sub[i] % 998244353 * frac_inv[n-i] for i in range(n+1)) % 998244353
ans = ans * pow(2, n, 998244353) * frac[n] % 998244353
print(ans)

try:
    x = input()
    assert x == ""
except EOFError:
    pass
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