This documentation is automatically generated by online-judge-tools/verification-helper
# verification-helper: PROBLEM https://judge.yosupo.jp/problem/convolution_mod
from pathlib import Path
import sys
sys.path.append(str(Path(__file__).resolve().parent.parent.parent.parent))
class NTT:
def __init__(self, MOD=998244353):
self.MOD = MOD
self.make_info(MOD)
def make_info(self, MOD):
g = self.primitive_root(MOD)
m = MOD - 1
rank2 = (m & -m).bit_length() - 1
root = [0] * (rank2 + 1)
iroot = [0] * (rank2 + 1)
rate2 = [0] * (rank2 + 1)
irate2 = [0] * (rank2 + 1)
rate3 = [0] * (rank2)
irate3 = [0] * (rank2)
root[rank2] = pow(g, (MOD - 1) >> rank2, MOD)
iroot[rank2] = pow(root[rank2], MOD - 2, MOD)
for i in range(rank2 - 1, -1, -1):
root[i] = root[i + 1] * root[i + 1] % MOD
iroot[i] = iroot[i + 1] * iroot[i + 1] % MOD
prod = 1
iprod = 1
for i in range(1, rank2):
rate2[i] = root[i + 1] * prod % MOD
irate2[i] = iroot[i + 1] * iprod % MOD
prod = prod * iroot[i + 1] % MOD
iprod = iprod * root[i + 1] % MOD
prod = 1
iprod = 1
for i in range(1, rank2 - 1):
rate3[i] = root[i + 2] * prod % MOD
irate3[i] = iroot[i + 2] * iprod % MOD
prod = prod * iroot[i + 2] % MOD
iprod = iprod * root[i + 2] % MOD
self.IMAG = rate2[1]
self.IIMAG = irate2[1]
self.rate2 = rate2
self.irate2 = irate2
self.rate3 = rate3
self.irate3 = irate3
def primitive_root(self, MOD):
if MOD == 998244353:
return 3
elif MOD == 200003:
return 2
elif MOD == 167772161:
return 3
elif MOD == 469762049:
return 3
elif MOD == 754974721:
return 11
divs = [0] * 20
divs[0] = 2
cnt = 1
x = (MOD - 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 1:
ok = True
for i in range(cnt):
if pow(g, (MOD - 1) // divs[i], MOD) == 1:
ok = False
break
if ok:
return g
g += 1
def butterfly(self, A):
n = len(A)
h = (n - 1).bit_length()
le = 0
while le < h:
if h - le == 1:
p = 1 << (h - le - 1)
rot = 1
for s in range(1 << le):
offset = s << (h - le)
for i in range(p):
l = A[i + offset]
r = A[i + offset + p] * rot
A[i + offset] = (l + r) % self.MOD
A[i + offset + p] = (l - r) % self.MOD
rot *= self.rate2[(~s & -~s).bit_length()]
rot %= self.MOD
le += 1
else:
p = 1 << (h - le - 2)
rot = 1
for s in range(1 << le):
rot2 = rot * rot % self.MOD
rot3 = rot2 * rot % self.MOD
offset = s << (h - le)
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) % self.MOD * self.IMAG
A[i + offset] = (a0 + a2 + a1 + a3) % self.MOD
A[i + offset + p] = (a0 + a2 - a1 - a3) % self.MOD
A[i + offset + p * 2] = (a0 - a2 + a1na3imag) % self.MOD
A[i + offset + p * 3] = (a0 - a2 - a1na3imag) % self.MOD
rot *= self.rate3[(~s & -~s).bit_length()]
rot %= self.MOD
le += 2
def butterfly_inv(self, A):
n = len(A)
h = (n - 1).bit_length()
le = h
while le:
if le == 1:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 1)):
offset = s << (h - le + 1)
for i in range(p):
l = A[i + offset]
r = A[i + offset + p]
A[i + offset] = (l + r) % self.MOD
A[i + offset + p] = (l - r) * irot % self.MOD
irot *= self.irate2[(~s & -~s).bit_length()]
irot %= self.MOD
le -= 1
else:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 2)):
irot2 = irot * irot % self.MOD
irot3 = irot2 * irot % self.MOD
offset = s << (h - le + 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) * self.IIMAG % self.MOD
A[i + offset] = (a0 + a1 + a2 + a3) % self.MOD
A[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % self.MOD
A[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % self.MOD
A[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % self.MOD
irot *= self.irate3[(~s & -~s).bit_length()]
irot %= self.MOD
le -= 2
def multiply(self, A, B):
n = len(A)
m = len(B)
if min(n, m) <= 60:
C = [0] * (n + m - 1)
for i in range(n):
if i % 8 == 0:
for j in range(m):
C[i + j] += A[i] * B[j]
C[i + j] %= self.MOD
else:
for j in range(m):
C[i + j] += A[i] * B[j]
return [c % self.MOD for c in C]
A = A[:]
B = B[:]
z = 1 << (n + m - 2).bit_length()
A += [0] * (z - n)
B += [0] * (z - m)
self.butterfly(A)
self.butterfly(B)
for i in range(z):
A[i] *= B[i]
A[i] %= self.MOD
self.butterfly_inv(A)
A = A[: n + m - 1]
iz = pow(z, self.MOD - 2, self.MOD)
return [a * iz % self.MOD for a in A]
n, m = map(int, input().split())
A = list(map(int, input().split()))
B = list(map(int, input().split()))
ntt = NTT()
C = ntt.multiply(A, B)
print(*C)Traceback (most recent call last):
File "/opt/hostedtoolcache/Python/3.11.4/x64/lib/python3.11/site-packages/onlinejudge_verify/documentation/build.py", line 81, in _render_source_code_stat
bundled_code = language.bundle(
^^^^^^^^^^^^^^^^
File "/opt/hostedtoolcache/Python/3.11.4/x64/lib/python3.11/site-packages/onlinejudge_verify/languages/python.py", line 108, in bundle
raise NotImplementedError
NotImplementedError