結果

問題 No.2243 Coaching Schedule
ユーザー shobonvipshobonvip
提出日時 2023-01-22 06:46:55
言語 PyPy3
(7.3.15)
結果
TLE  
実行時間 -
コード長 7,491 bytes
コンパイル時間 216 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 266,688 KB
最終ジャッジ日時 2024-09-18 03:00:23
合計ジャッジ時間 6,779 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge3
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 69 ms
79,728 KB
testcase_01 AC 67 ms
78,976 KB
testcase_02 AC 69 ms
79,488 KB
testcase_03 AC 68 ms
77,824 KB
testcase_04 AC 69 ms
80,256 KB
testcase_05 TLE -
testcase_06 TLE -
testcase_07 TLE -
testcase_08 TLE -
testcase_09 TLE -
testcase_10 TLE -
testcase_11 TLE -
testcase_12 TLE -
testcase_13 TLE -
testcase_14 TLE -
testcase_15 TLE -
testcase_16 AC 2,311 ms
258,120 KB
testcase_17 AC 1,528 ms
142,928 KB
testcase_18 TLE -
testcase_19 TLE -
testcase_20 AC 2,756 ms
206,388 KB
testcase_21 AC 2,276 ms
182,368 KB
testcase_22 AC 2,133 ms
175,524 KB
testcase_23 AC 626 ms
106,944 KB
testcase_24 AC 2,744 ms
199,248 KB
testcase_25 AC 775 ms
113,376 KB
testcase_26 AC 1,311 ms
134,596 KB
testcase_27 AC 2,738 ms
204,932 KB
testcase_28 AC 831 ms
114,648 KB
testcase_29 AC 3,723 ms
260,512 KB
testcase_30 TLE -
testcase_31 TLE -
testcase_32 AC 2,043 ms
171,452 KB
testcase_33 AC 1,404 ms
139,496 KB
testcase_34 AC 3,651 ms
254,828 KB
testcase_35 TLE -
testcase_36 TLE -
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 # 

from collections import deque

# 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)

# ----

def poly_inv(a, length = None):
	if length == None: M = len(a)
	else: M = length
	if length <= 0: return []
	n = len(a)
	r = pow(a[0], _fft_mod-2, _fft_mod)
	m = 1
	res = [r]
	while m < M:
		f = a[:min(n,2*m)] + [0]*(2*m-min(n,2*m))
		g = res + [0]*m
		_butterfly(f)
		_butterfly(g)
		for i in range(2*m):
			f[i] = f[i] * g[i] % _fft_mod
		_butterfly_inv(f)
		f = f[m:] + [0]*m
		_butterfly(f)
		for i in range(2*m):
			f[i] = f[i] * g[i] % _fft_mod
		_butterfly_inv(f)
		iz = pow(2*m, _fft_mod-2, _fft_mod)
		iz = (-iz*iz) % _fft_mod
		for i in range(m):
			f[i] = f[i] * iz % _fft_mod
		res += f[:m]
		m <<= 1
	return res[:M]

def multi_eval(x, a):
	n = len(x)
	siz = 1 << (n-1).bit_length()

	g = [[1] for i in range(2 * siz)]

	for i in range(n):
		g[i + siz] = [-x[i], 1]

	for i in range(siz-1, 0, -1):
		g[i] = convolution(g[2 * i], g[2 * i + 1])
	
	for i in range(1, 2 * siz):
		if i == 1: f = a[::]
		else: f = g[i >> 1]
		m = len(f) - len(g[i]) + 1
		#print(g[i])
		v = convolution(f[::-1][:m], poly_inv(g[i][::-1], m))[m-1::-1]
		w = convolution(v, g[i])
		g[i] = f[::]
		h = g[i]

		for j in range(len(w)):
			h[j] -= w[j]
			h[j] %= _fft_mod
		
		while len(h) > 1 and h[-1] == 0:
			h.pop()
	
	return [g[i+siz][0] for i in range(n)]


mod = 998244353
N = 10**6 + 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

# ここから本編.

m,n = map(int,input().split())
a = list(map(int,input().split()))

# 頻度ごとに集計しています O(N+M)
c = [0] * m
for i in range(n):
    c[a[i]-1] += 1

# (x-なんとか) の積を多項式マージテクで計算します O(M log^2 M)
dq = deque()
r = 0
for i in range(m):
	for j in range(c[i]):
		dq.append([-j, 1])
	r = max(r, c[i])

while len(dq) > 1:
	f1 = dq.popleft()
	f2 = dq.popleft()
	dq.append(convolution(f1, f2))

# Multipoint Evaluation を用いて, f(0),...,f(n) の値を計算します O(M log^2 M)
h = dq.popleft()
d = multi_eval([i for i in range(n+1)], h)

# またまたFFTによって練習の日を固定したときの数え上げを計算します O(N log N)

f = [d[i] * factinv[i] % mod for i in range(n + 1)]
g = [(-1) ** (i % 2) * factinv[i] % mod for i in range(n + 1)]
fg = convolution(f, g)

ans = 0

for i in range(n + 1):
	ans += fact[i] * fg[i] % mod

print(ans % mod)

# 計 : O(M log^2 M + N log N)
0