結果
| 問題 |
No.2303 Frog on Grid
|
| コンテスト | |
| ユーザー |
 Shirotsume
|
| 提出日時 | 2023-04-03 13:46:57 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
WA
(最新)
AC
(最初)
|
| 実行時間 | - |
| コード長 | 8,556 bytes |
| コンパイル時間 | 182 ms |
| コンパイル使用メモリ | 82,120 KB |
| 実行使用メモリ | 105,816 KB |
| 最終ジャッジ日時 | 2024-10-02 02:36:41 |
| 合計ジャッジ時間 | 5,094 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | WA * 3 |
| other | AC * 1 WA * 19 |
ソースコード
"""
Reference
https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp
https://github.com/atcoder/ac-library/blob/master/atcoder/internal_math.hpp
https://github.com/atcoder/ac-library/blob/master/document_en/convolution.md
https://github.com/atcoder/ac-library/blob/master/document_ja/convolution.md
"""
mod = 998244353
def primitive_root(m):
if m == 2:
return 1
if m == 167772161:
return 3
if m == 469762049:
return 3
if m == 754974721:
return 11
if m == 998244353:
return 3
divs = [0] * 20
divs[0] = 2
cnt = 1
x = (m - 1) // 2
while x % 2 == 0:
x //= 2
i = 3
while i * i <= x:
if x % i == 0:
divs[cnt] = i
cnt += 1
while x % i == 0:
x //= i
i += 2
if x > 1:
divs[cnt] = x
cnt += 1
g = 2
while True:
ok = True
for i in range(cnt):
if pow(g, (m - 1) // divs[i], m) == 1:
ok = False
break
if ok:
return g
g += 1
class FFT_INFO:
def __init__(self):
self.g = primitive_root(mod)
self.rank2 = ((mod - 1) & (1 - mod)).bit_length() - 1
self.root = [0] * (self.rank2 + 1)
self.root[self.rank2] = pow(self.g, (mod - 1) >> self.rank2, mod)
self.iroot = [0] * (self.rank2 + 1)
self.iroot[self.rank2] = pow(self.root[self.rank2], mod - 2, mod)
for i in range(self.rank2 - 1, -1, -1):
self.root[i] = self.root[i + 1] * self.root[i + 1] % mod
self.iroot[i] = self.iroot[i + 1] * self.iroot[i + 1] % mod
self.rate2 = [0] * max(0, self.rank2 - 1)
self.irate2 = [0] * max(0, self.rank2 - 1)
prod = 1
iprod = 1
for i in range(self.rank2 - 1):
self.rate2[i] = self.root[i + 2] * prod % mod
self.irate2[i] = self.iroot[i + 2] * iprod % mod
prod *= self.iroot[i + 2]
prod %= mod
iprod *= self.root[i + 2]
iprod %= mod
self.rate3 = [0] * max(0, self.rank2 - 2)
self.irate3 = [0] * max(0, self.rank2 - 2)
prod = 1
iprod = 1
for i in range(self.rank2 - 2):
self.rate3[i] = self.root[i + 3] * prod % mod
self.irate3[i] = self.iroot[i + 3] * iprod % mod
prod *= self.iroot[i + 3]
prod %= mod
iprod *= self.root[i + 3]
iprod %= mod
info = FFT_INFO()
def butterfly(a):
n = len(a)
h = (n - 1).bit_length()
length = 0
while length < h:
if h - length == 1:
p = 1 << (h - length - 1)
rot = 1
for s in range(1 << length):
offset = s << (h - length)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p] * rot % mod
a[i + offset] = (l + r) % mod
a[i + offset + p] = (l - r) % mod
if s + 1 != (1 << length):
rot *= info.rate2[(~s & -~s).bit_length() - 1]
rot %= mod
length += 1
else:
# 4-base
p = 1 << (h - length - 2)
rot = 1
imag = info.root[2]
for s in range(1 << length):
rot2 = rot * rot % mod
rot3 = rot2 * rot % mod
offset = s << (h - length)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p] * rot
a2 = a[i + offset + 2 * p] * rot2
a3 = a[i + offset + 3 * p] * rot3
a1na3imag = (a1 - a3) % mod * imag
a[i + offset] = (a0 + a2 + a1 + a3) % mod
a[i + offset + p] = (a0 + a2 - a1 - a3) % mod
a[i + offset + 2 * p] = (a0 - a2 + a1na3imag) % mod
a[i + offset + 3 * p] = (a0 - a2 - a1na3imag) % mod
if s + 1 != (1 << length):
rot *= info.rate3[(~s & -~s).bit_length() - 1]
rot %= mod
length += 2
def butterfly_inv(a):
n = len(a)
h = (n - 1).bit_length()
length = h # a[i, i+(n<<length), i+2*(n>>length), ...] is transformed
while length:
if length == 1:
p = 1 << (h - length)
irot = 1
for s in range(1 << (length - 1)):
offset = s << (h - length + 1)
for i in range(p):
l = a[i + offset]
r = a[i + offset + p]
a[i + offset] = (l + r) % mod
a[i + offset + p] = (l - r) * irot % mod
if s + 1 != (1 << (length - 1)):
irot *= info.irate2[(~s & -~s).bit_length() - 1]
irot %= mod
length -= 1
else:
# 4-base
p = 1 << (h - length)
irot = 1
iimag = info.iroot[2]
for s in range(1 << (length - 2)):
irot2 = irot * irot % mod
irot3 = irot2 * irot % mod
offset = s << (h - length + 2)
for i in range(p):
a0 = a[i + offset]
a1 = a[i + offset + p]
a2 = a[i + offset + 2 * p]
a3 = a[i + offset + 3 * p]
a2na3iimag = (a2 - a3) * iimag % mod
a[i + offset] = (a0 + a1 + a2 + a3) % mod
a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % mod
a[i + offset + 2 * p] = (a0 + a1 - a2 - a3) * irot2 % mod
a[i + offset + 3 * p] = (a0 - a1 - a2na3iimag) * irot3 % mod
if s + 1 != (1 << (length - 2)):
irot *= info.irate3[(~s & -~s).bit_length() - 1]
irot %= mod
length -= 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] += a[i] * b[j]
ans[i + j] %= mod
else:
for i in range(n):
for j in range(m):
ans[i + j] += a[i] * b[j]
ans[i + j] %= 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] *= b[i]
a[i] %= mod
butterfly_inv(a)
a = a[:n + m - 1]
iz = pow(z, mod - 2, mod)
for i in range(n + m - 1):
a[i] *= iz
a[i] %= mod
return a
def convolution(a, b):
n = len(a)
m = len(b)
if not n or not m:
return []
if min(n, m) <= 60:
return convolution_naive(a, b)
return convolution_fft(a, b)
class Combinatorics():
def __init__(self, mod, maxi):
self.mod = mod
self.maxi = maxi
self.facs = [1] * (maxi + 1)
self.factinvs = [1] * (maxi + 1)
self.invs = [1] * (maxi + 1)
for i in range(2, self.maxi + 1):
self.facs[i] = ((self.facs[i-1] * i) % self.mod)
self.invs[i] = (-self.invs[self.mod % i] * (self.mod // i)) % self.mod
self.factinvs[i] = (self.factinvs[i-1] * self.invs[i]) % self.mod
def choose(self, n, k) -> int:
if k < 0 or k > n: return 0
if k == 0 or k == n: return 1
k = min(k, n - k)
return (((self.facs[n] * self.factinvs[k]) % self.mod) * self.factinvs[n-k]) % self.mod
def perm(self, n, k) -> int:
return (self.choose(n, k) * self.facs[k]) % self.mod
def homop(self, n, k) -> int:
if n == k == 0:
return 1
return self.choose(n + k - 1, k)
import sys
from collections import deque, Counter
input = lambda: sys.stdin.readline().rstrip()
ii = lambda: int(input())
mi = lambda: map(int, input().split())
li = lambda: list(mi())
inf = 2 ** 63 - 1
mod = 998244353
C = Combinatorics(mod, 5 * 10 ** 5)
h, w = mi()
H = []
W = []
for i in range(h // 2 + 1):
H.append(C.factinvs[i] * C.factinvs[h - 2 * i] % mod)
for i in range(w // 2 + 1):
W.append(C.factinvs[i] * C.factinvs[w - 2 * i] % mod)
F = convolution(H, W)
ans = 0
for i in range(len(F)):
ans += C.facs[h + w - 2 * i] * F[i]
ans %= mod
print(ans)