結果
| 問題 | No.2097 AND^k |
| ユーザー |
 chineristAC
|
| 提出日時 | 2022-09-21 23:29:02 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 2,016 ms / 5,000 ms |
| コード長 | 9,670 bytes |
| コンパイル時間 | 288 ms |
| コンパイル使用メモリ | 87,128 KB |
| 実行使用メモリ | 255,360 KB |
| 最終ジャッジ日時 | 2023-08-23 20:13:27 |
| 合計ジャッジ時間 | 26,195 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge11 |
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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 | 146 ms
88,764 KB |
| testcase_01 | AC | 145 ms
88,780 KB |
| testcase_02 | AC | 146 ms
88,472 KB |
| testcase_03 | AC | 160 ms
89,180 KB |
| testcase_04 | AC | 171 ms
90,112 KB |
| testcase_05 | AC | 150 ms
88,316 KB |
| testcase_06 | AC | 148 ms
88,404 KB |
| testcase_07 | AC | 157 ms
89,000 KB |
| testcase_08 | AC | 844 ms
171,416 KB |
| testcase_09 | AC | 531 ms
137,196 KB |
| testcase_10 | AC | 883 ms
172,816 KB |
| testcase_11 | AC | 502 ms
133,836 KB |
| testcase_12 | AC | 471 ms
129,460 KB |
| testcase_13 | AC | 1,668 ms
254,100 KB |
| testcase_14 | AC | 1,594 ms
255,360 KB |
| testcase_15 | AC | 1,831 ms
254,248 KB |
| testcase_16 | AC | 1,428 ms
250,268 KB |
| testcase_17 | AC | 1,772 ms
254,216 KB |
| testcase_18 | AC | 1,551 ms
254,304 KB |
| testcase_19 | AC | 1,499 ms
253,800 KB |
| testcase_20 | AC | 1,412 ms
250,260 KB |
| testcase_21 | AC | 1,424 ms
250,096 KB |
| testcase_22 | AC | 1,538 ms
253,884 KB |
| testcase_23 | AC | 1,495 ms
254,928 KB |
| testcase_24 | AC | 145 ms
88,668 KB |
| testcase_25 | AC | 2,016 ms
254,200 KB |
ソースコード
mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)
N = 2*10**5
g1 = [1]*(N+1) # 元テーブル
g2 = [1]*(N+1) #逆元テーブル
inv = [1]*(N+1) #逆元テーブル計算用テーブル
for i in range( 2, N + 1 ):
g1[i]=( ( g1[i-1] * i ) % mod )
inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )
g2[i]=( (g2[i-1] * inv[i]) % mod )
inv[0]=0
def _ntt(f,L,reverse=False):
F=[f[i] for i in range(L)]
n = L.bit_length() - 1
base = omega
if reverse:
base = rev_omega
if not n:
return F
size = 2**n
wj = pow(base,2**22,mod)
res = [0]*2**n
for i in range(n,0,-1):
use_omega = pow(base,2**(22+i-n),mod)
res = [0]*2**n
size //= 2
w = 1
for j in range(0,L//2,size):
for a in range(size):
res[a+j] = (F[a+2*j] + w * F[a+size+2*j]) % mod
t = (w * wj) % mod
res[L//2+a+j] = (F[a+2*j] + t * F[a+size+2*j]) % mod
w = (w * use_omega) % mod
F = res
return res
def ntt(f,L=0):
l = len(f)
if not L:
L = 1<<((l-1).bit_length())
while len(f)<L:
f.append(0)
f=f[:L]
F = _ntt(f,L)
return F
def intt(f,L=0):
l = len(f)
if not L:
L = 1<<((l-1).bit_length())
while len(f)<L:
f.append(0)
f=f[:L]
F = _ntt(f,L,reverse=True)
inv = pow(L,mod-2,mod)
for i in range(L):
F[i] *= inv
F[i] %= mod
return F
def convolve(_f,_g,limit):
f = [v for v in _f]
g = [v for v in _g]
l = len(f)+len(g)-1
L = 1<<((l-1).bit_length())
F = ntt(f,L)
G = ntt(g,L)
H = [(F[i] * G[i]) % mod for i in range(L)]
h = intt(H,L)
return h[:limit]
mod = 998244353
omega = pow(3,119,mod)
rev_omega = pow(omega,mod-2,mod)
N = 2*10**5
g1 = [1]*(N+1) # 元テーブル
g2 = [1]*(N+1) #逆元テーブル
inv = [1]*(N+1) #逆元テーブル計算用テーブル
for i in range( 2, N + 1 ):
g1[i]=( ( g1[i-1] * i ) % mod )
inv[i]=( ( -inv[mod % i] * (mod//i) ) % mod )
g2[i]=( (g2[i-1] * inv[i]) % mod )
inv[0]=0
_fft_mod = 998244353
_fft_imag = 911660635
_fft_iimag = 86583718
_fft_rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)
_fft_irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,
354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)
_fft_rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,
183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)
_fft_irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,
771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)
def _butterfly(a):
n = len(a)
h = (n - 1).bit_length()
len_ = 0
while len_ < h:
if h - len_ == 1:
p = 1 << (h - len_ - 1)
rot = 1
for s in range(1 << len_):
offset = s << (h - len_)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p] * rot % _fft_mod
a[i + offset] = (l + r) % _fft_mod
a[i + offset + p] = (l - r) % _fft_mod
if s + 1 != (1 << len_):
rot *= _fft_rate2[(~s & -~s).bit_length() - 1]
rot %= _fft_mod
len_ += 1
else:
p = 1 << (h - len_ - 2)
rot = 1
for s in range(1 << len_):
rot2 = rot * rot % _fft_mod
rot3 = rot2 * rot % _fft_mod
offset = s << (h - len_)
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) % _fft_mod * _fft_imag
a[i + offset] = (a0 + a2 + a1 + a3) % _fft_mod
a[i + offset + p] = (a0 + a2 - a1 - a3) % _fft_mod
a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % _fft_mod
a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % _fft_mod
if s + 1 != (1 << len_):
rot *= _fft_rate3[(~s & -~s).bit_length() - 1]
rot %= _fft_mod
len_ += 2
def _butterfly_inv(a):
n = len(a)
h = (n - 1).bit_length()
len_ = h
while len_:
if len_ == 1:
p = 1 << (h - len_)
irot = 1
for s in range(1 << (len_ - 1)):
offset = s << (h - len_ + 1)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p]
a[i + offset] = (l + r) % _fft_mod
a[i + offset + p] = (l - r) * irot % _fft_mod
if s + 1 != (1 << (len_ - 1)):
irot *= _fft_irate2[(~s & -~s).bit_length() - 1]
irot %= _fft_mod
len_ -= 1
else:
p = 1 << (h - len_)
irot = 1
for s in range(1 << (len_ - 2)):
irot2 = irot * irot % _fft_mod
irot3 = irot2 * irot % _fft_mod
offset = s << (h - len_ + 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) * _fft_iimag % _fft_mod
a[i + offset] = (a0 + a1 + a2 + a3) % _fft_mod
a[i + offset + p] = (a0 - a1 +
a2na3iimag) * irot % _fft_mod
a[i + offset + p * 2] = (a0 + a1 -
a2 - a3) * irot2 % _fft_mod
a[i + offset + p * 3] = (a0 - a1 -
a2na3iimag) * irot3 % _fft_mod
if s + 1 != (1 << (len_ - 1)):
irot *= _fft_irate3[(~s & -~s).bit_length() - 1]
irot %= _fft_mod
len_ -= 2
def _convolution_naive(a, b):
n = len(a)
m = len(b)
ans = [0] * (n + m - 1)
if n < m:
for j in range(m):
for i in range(n):
ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
else:
for i in range(n):
for j in range(m):
ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
return ans
def _convolution_fft(a, b):
a = a.copy()
b = b.copy()
n = len(a)
m = len(b)
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
_butterfly(a)
b += [0] * (z - m)
_butterfly(b)
for i in range(z):
a[i] = a[i] * b[i] % _fft_mod
_butterfly_inv(a)
a = a[:n + m - 1]
iz = pow(z, _fft_mod - 2, _fft_mod)
for i in range(n + m - 1):
a[i] = a[i] * iz % _fft_mod
return a
def _convolution_square(a):
a = a.copy()
n = len(a)
z = 1 << (2 * n - 2).bit_length()
a += [0] * (z - n)
_butterfly(a)
for i in range(z):
a[i] = a[i] * a[i] % _fft_mod
_butterfly_inv(a)
a = a[:2 * n - 1]
iz = pow(z, _fft_mod - 2, _fft_mod)
for i in range(2 * n - 1):
a[i] = a[i] * iz % _fft_mod
return a
def convolution(a, b):
"""It calculates (+, x) convolution in mod 998244353.
Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1],
it calculates the array c of length n + m - 1, defined by
> c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.
It returns an empty list if at least one of a and b are empty.
Constraints
-----------
> len(a) + len(b) <= 8388609
Complexity
----------
> O(n log n), where n = len(a) + len(b).
"""
n = len(a)
m = len(b)
if n == 0 or m == 0:
return []
if min(n, m) <= 0:
return _convolution_naive(a, b)
if a is b:
return _convolution_square(a)
return _convolution_fft(a, b)
import sys,random,bisect
from collections import deque,defaultdict
from heapq import heapify,heappop,heappush
from itertools import permutations
from math import log,gcd
input = lambda :sys.stdin.readline()
mi = lambda :map(int,input().split())
li = lambda :list(mi())
def calc(N,M,L):
if M==1:
res = [g2[i] for i in range(L+1)]
res[0] += pow(2,N,mod) - 1
res[0] %= mod
return res
m = M//2
f = calc(N,m,L)
g = f.copy()
t = pow(2,m,mod)
p = 1
for i in range(L+1):
g[i] = g[i] * p % mod
p = p * t % mod
res = convolution(f,g)[:L+1]
if M&1:
t = pow(2,M-1,mod)
p = 1
h = [0] * (L+1)
for i in range(L+1):
h[i] = p * g2[i] % mod
p = p * t % mod
h[0] += pow(2,N,mod) - 1
h[0] %= mod
res = convolution(res,h)[:L+1]
return res
N,M,L = mi()
res = calc(N,M,L)
for i in range(1,L+1):
print(res[i] * g1[i] % mod)