結果
| 問題 | No.2413 Multiple of 99 |
| ユーザー |
 Ricky_pon
|
| 提出日時 | 2023-07-21 13:05:00 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,126 ms / 8,000 ms |
| コード長 | 6,499 bytes |
| コンパイル時間 | 269 ms |
| コンパイル使用メモリ | 82,272 KB |
| 実行使用メモリ | 208,680 KB |
| 最終ジャッジ日時 | 2024-09-21 15:08:43 |
| 合計ジャッジ時間 | 14,554 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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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 | 39 ms
53,376 KB |
| testcase_01 | AC | 40 ms
53,248 KB |
| testcase_02 | AC | 44 ms
54,784 KB |
| testcase_03 | AC | 44 ms
52,992 KB |
| testcase_04 | AC | 97 ms
77,064 KB |
| testcase_05 | AC | 129 ms
79,776 KB |
| testcase_06 | AC | 111 ms
79,220 KB |
| testcase_07 | AC | 1,074 ms
208,168 KB |
| testcase_08 | AC | 38 ms
52,992 KB |
| testcase_09 | AC | 1,089 ms
208,548 KB |
| testcase_10 | AC | 1,126 ms
208,680 KB |
| testcase_11 | AC | 1,059 ms
208,296 KB |
| testcase_12 | AC | 1,070 ms
208,164 KB |
| testcase_13 | AC | 1,068 ms
208,552 KB |
| testcase_14 | AC | 1,069 ms
208,292 KB |
| testcase_15 | AC | 1,068 ms
208,528 KB |
| testcase_16 | AC | 568 ms
142,532 KB |
| testcase_17 | AC | 560 ms
139,000 KB |
| testcase_18 | AC | 1,073 ms
202,652 KB |
| testcase_19 | AC | 182 ms
86,092 KB |
| testcase_20 | AC | 134 ms
81,008 KB |
| testcase_21 | AC | 154 ms
83,032 KB |
| testcase_22 | AC | 1,051 ms
203,624 KB |
| testcase_23 | AC | 209 ms
89,364 KB |
ソースコード
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 = 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()