結果
| 問題 |
No.2243 Coaching Schedule
|
| コンテスト | |
| ユーザー |
 shobonvip
|
| 提出日時 | 2023-03-09 17:42:46 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 8,948 bytes |
| コンパイル時間 | 165 ms |
| コンパイル使用メモリ | 82,292 KB |
| 実行使用メモリ | 116,908 KB |
| 最終ジャッジ日時 | 2024-09-18 02:56:40 |
| 合計ジャッジ時間 | 16,485 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | WA * 37 |
ソースコード
import os
import sys
from io import BytesIO, IOBase
BUFSIZE = 8192
class FastIO(IOBase):
newlines = 0
def __init__(self, file):
self._fd = file.fileno()
self.buffer = BytesIO()
self.writable = "x" in file.mode or "r" not in file.mode
self.write = self.buffer.write if self.writable else None
def read(self):
while True:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
if not b:
break
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines = 0
return self.buffer.read()
def readline(self):
while self.newlines == 0:
b = os.read(self._fd, max(os.fstat(self._fd).st_size, BUFSIZE))
self.newlines = b.count(b"\n")+(not b)
ptr = self.buffer.tell()
self.buffer.seek(0, 2), self.buffer.write(b), self.buffer.seek(ptr)
self.newlines -= 1
return self.buffer.readline()
def flush(self):
if self.writable:
os.write(self._fd, self.buffer.getvalue())
self.buffer.truncate(0), self.buffer.seek(0)
class IOWrapper(IOBase):
def __init__(self, file):
self.buffer = FastIO(file)
self.flush = self.buffer.flush
self.writable = self.buffer.writable
self.write = lambda s:self.buffer.write(s.encode("ascii"))
self.read = lambda:self.buffer.read().decode("ascii")
self.readline = lambda:self.buffer.readline().decode("ascii")
sys.stdin, sys.stdout = IOWrapper(sys.stdin), IOWrapper(sys.stdout)
input = lambda:sys.stdin.readline().rstrip("\r\n")
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
import time
# ここから本編.
m,n = map(int,input().split())
a = list(map(int,input().split()))
st = time.time()
# 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
cl = [0] * (n+1)
for i in range(m):
cl[c[i]] += 1
cv = []
cmax = 0
for i in range(n+1):
if cl[i] > 0:
cv.append((i, cl[i]))
cmax = max(cmax, i)
# 想定解通りにやります O(N^1.5 log N) ? わからんぬ
d = [1] * (n+1)
for i in range(n+1):
if cmax > i:
d[i] = 0
continue
for j, cnt in cv:
d[i] *= pow(fact[i] * factinv[i-j] % mod, cnt, mod)
d[i] %= mod
# 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)
print(time.time() - st)