結果

問題 No.2237 Xor Sum Hoge
ユーザー shobonvipshobonvip
提出日時 2023-03-03 22:02:47
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 5,391 ms / 10,000 ms
コード長 5,997 bytes
コンパイル時間 2,047 ms
コンパイル使用メモリ 81,500 KB
実行使用メモリ 275,620 KB
最終ジャッジ日時 2023-10-18 02:08:57
合計ジャッジ時間 127,477 ms
ジャッジサーバーID
（参考情報） 		judge14 / judge11
このコードへのチャレンジ
（要ログイン）

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 4,181 ms
267,536 KB
testcase_01 AC 2,310 ms
260,300 KB
testcase_02 AC 2,307 ms
260,156 KB
testcase_03 AC 2,249 ms
260,156 KB
testcase_04 AC 2,318 ms
260,156 KB
testcase_05 AC 2,319 ms
260,972 KB
testcase_06 AC 2,267 ms
260,852 KB
testcase_07 AC 2,310 ms
260,980 KB
testcase_08 AC 2,316 ms
260,980 KB
testcase_09 AC 2,319 ms
260,980 KB
testcase_10 AC 2,258 ms
261,644 KB
testcase_11 AC 2,321 ms
262,860 KB
testcase_12 AC 4,145 ms
271,624 KB
testcase_13 AC 4,170 ms
270,572 KB
testcase_14 AC 4,171 ms
274,484 KB
testcase_15 AC 4,251 ms
267,940 KB
testcase_16 AC 4,266 ms
270,480 KB
testcase_17 AC 4,269 ms
272,600 KB
testcase_18 AC 4,161 ms
268,456 KB
testcase_19 AC 4,144 ms
264,828 KB
testcase_20 AC 4,251 ms
273,332 KB
testcase_21 AC 4,282 ms
272,328 KB
testcase_22 AC 4,280 ms
271,932 KB
testcase_23 AC 4,190 ms
271,208 KB
testcase_24 AC 4,182 ms
273,560 KB
testcase_25 AC 4,280 ms
272,508 KB
testcase_26 AC 5,391 ms
272,764 KB
testcase_27 AC 4,390 ms
272,464 KB
testcase_28 AC 4,173 ms
274,808 KB
testcase_29 AC 4,174 ms
272,500 KB
testcase_30 AC 4,313 ms
275,620 KB
testcase_31 AC 2,260 ms
261,092 KB
testcase_32 AC 2,275 ms
261,148 KB
testcase_33 AC 2,297 ms
261,680 KB
testcase_34 AC 2,274 ms
260,908 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 # 

# FFT
# code from: https://atcoder.jp/contests/practice2/submissions/24974537
# but changed a little
_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):
	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)
# ----

mod = 998244353
N = 3 * 10**5 + 5
fact = [1]*(N+1)
factinv = [1]*(N+1)

for i in range(2, N+1):
	fact[i] = fact[i-1] * i % mod

factinv[-1] = pow(fact[-1], mod-2, mod)
for i in range(N-1, 1, -1):
	factinv[i] = factinv[i+1] * (i+1) % mod

def cmb(a, b):
	if (a < b) or (b < 0):
		return 0
	return fact[a] * factinv[b] % mod * factinv[a-b] % mod


n,b,c = map(int,input().split())

# 下から決めていく

# dp[i][j] : 下から i 桁決めたとき, 余りが j (かならず 1.2×10^5 以下)

dp = [[0] * 120001 for i in range(80)]
dp[0][0] = 1

# 0, cmb(n, 1), cmb(n, 2), ..., n を加算する！

ar0 = [0] * (n+1)
ar1 = [0] * (n+1)
for i in range(n+1):
	if i % 2 == 0:
		ar0[i] = cmb(n, i)
	else:
		ar1[i] = cmb(n, i)

for num in range(79):
	for i in range(120001):
		dp[num+1][i//2] += dp[num][i]
		dp[num+1][i//2] %= mod
	if (c >> num) & 1:
		dp[num+1] = convolution(dp[num+1], ar1)[:120001]
	else:
		dp[num+1] = convolution(dp[num+1], ar0)[:120001]

	for i in range(120001):
		if (i & 1) != (b >> num) & 1:
			dp[num+1][i] = 0
		if i > (b >> num):
			dp[num+1][i] = 0
		

print(dp[79][0])
0