結果
| 問題 | No.1760 Setwise Coprime |
| ユーザー |
 chineristAC
|
| 提出日時 | 2021-11-20 18:12:32 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 246 ms / 2,000 ms |
| コード長 | 9,174 bytes |
| コンパイル時間 | 287 ms |
| コンパイル使用メモリ | 86,856 KB |
| 実行使用メモリ | 96,304 KB |
| 最終ジャッジ日時 | 2023-09-02 14:05:42 |
| 合計ジャッジ時間 | 9,814 ms |
|
ジャッジサーバーID （参考情報） |
judge15 / judge14 |
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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 | 160 ms
86,368 KB |
| testcase_01 | AC | 161 ms
86,040 KB |
| testcase_02 | AC | 185 ms
87,012 KB |
| testcase_03 | AC | 161 ms
86,332 KB |
| testcase_04 | AC | 161 ms
86,244 KB |
| testcase_05 | AC | 161 ms
86,360 KB |
| testcase_06 | AC | 182 ms
87,292 KB |
| testcase_07 | AC | 179 ms
86,964 KB |
| testcase_08 | AC | 181 ms
87,060 KB |
| testcase_09 | AC | 180 ms
87,308 KB |
| testcase_10 | AC | 167 ms
86,800 KB |
| testcase_11 | AC | 180 ms
86,840 KB |
| testcase_12 | AC | 178 ms
87,008 KB |
| testcase_13 | AC | 160 ms
86,308 KB |
| testcase_14 | AC | 181 ms
87,268 KB |
| testcase_15 | AC | 179 ms
87,176 KB |
| testcase_16 | AC | 178 ms
87,080 KB |
| testcase_17 | AC | 177 ms
87,140 KB |
| testcase_18 | AC | 168 ms
86,684 KB |
| testcase_19 | AC | 179 ms
87,164 KB |
| testcase_20 | AC | 180 ms
87,084 KB |
| testcase_21 | AC | 233 ms
94,448 KB |
| testcase_22 | AC | 221 ms
93,704 KB |
| testcase_23 | AC | 232 ms
95,416 KB |
| testcase_24 | AC | 202 ms
90,872 KB |
| testcase_25 | AC | 222 ms
94,188 KB |
| testcase_26 | AC | 213 ms
92,700 KB |
| testcase_27 | AC | 195 ms
89,260 KB |
| testcase_28 | AC | 188 ms
87,980 KB |
| testcase_29 | AC | 235 ms
95,704 KB |
| testcase_30 | AC | 234 ms
95,616 KB |
| testcase_31 | AC | 195 ms
89,788 KB |
| testcase_32 | AC | 226 ms
94,768 KB |
| testcase_33 | AC | 215 ms
92,568 KB |
| testcase_34 | AC | 234 ms
95,784 KB |
| testcase_35 | AC | 228 ms
93,896 KB |
| testcase_36 | AC | 240 ms
96,272 KB |
| testcase_37 | AC | 246 ms
95,960 KB |
| testcase_38 | AC | 244 ms
96,304 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
inverse = [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 )
inverse[i]=( ( -inverse[mod % i] * (mod//i) ) % mod )
g2[i]=( (g2[i-1] * inverse[i]) % mod )
inverse[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)
def cmb(n, r, mod):
if ( r<0 or r>n ):
return 0
r = min(r, n-r)
return g1[n] * g2[r] * g2[n-r] % mod
class SegmentTree:
def __init__(self, init_val, segfunc, ide_ele):
n = len(init_val)
self.segfunc = segfunc
self.ide_ele = ide_ele
self.num = 1 << (n - 1).bit_length()
self.tree = [ide_ele] * 2 * self.num
self.size = n
for i in range(n):
self.tree[self.num + i] = init_val[i]
for i in range(self.num - 1, 0, -1):
self.tree[i] = self.segfunc(self.tree[2 * i], self.tree[2 * i + 1])
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())
mod = 998244353
M = 2*10**5
i4 = pow(4,mod-2,mod)
def zeta(N,_A):
A = [_A[i] for i in range(N+1)]
sieve = [True for i in range(N+1)]
for i in range(2,N+1):
if not sieve[i]:
continue
for j in range(1,N//i+1):
sieve[i*j] = False
A[j*i] += A[j]
A[j*i] %= mod
return A
def mebius(N,_A):
A = [_A[i] for i in range(N+1)]
sieve = [True for i in range(N+1)]
for i in range(2,N+1):
if not sieve[i]:
continue
for j in range(1,N//i+1)[::-1]:
sieve[i*j] = False
A[j*i] -= A[j]
A[j*i] %= mod
return A
Mebius = [1 for i in range(M+1)]
sieve = [True for i in range(M+1)]
for i in range(2,M+1):
if not sieve[i]:continue
for j in range(i,M+1,i):
sieve[j] = False
if j%(i*i)==0:
Mebius[j] = 0
Mebius[j] *= -1
N = int(input())
A = [0] + [Mebius[i]*pow(2,N//i,mod) for i in range(1,N+1)]
#print(A)
zA = zeta(N,A)
#print(zA)
for i in range(N+1):
zA[i] = zA[i] * zA[i] % mod
#print(zA)
mzA = mebius(N,zA)
#print(mzA)
res = 0
for lcm in range(1,N+1):
res += mzA[lcm] * pow(3*i4,N//lcm,mod) % mod
res %= mod
rest = sum(A)**2 - sum(mzA) % mod
rest %= mod
res += rest
res %= mod
C = sum(Mebius[1:N+1])
res += -2 * C * sum(A) + C * C
res %= mod
print(res)