結果
| 問題 | No.3619 Compositional Power with Schröder Coordinate |
| コンテスト | |
| ユーザー |
 Mogobon
|
| 提出日時 | 2026-08-10 22:58:27 |
| 言語 | PyPy3 (7.3.17) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 21,963 bytes |
| 記録 | |
| コンパイル時間 | 270 ms |
| コンパイル使用メモリ | 95,468 KB |
| 実行使用メモリ | 872,224 KB |
| 最終ジャッジ日時 | 2026-08-10 22:59:21 |
| 合計ジャッジ時間 | 14,011 ms |
|
ジャッジサーバーID （参考情報） |
judge1_0 / judge2_0 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 1 TLE * 1 -- * 4 |
ソースコード
# https://github.com/lif4635/harurun-s-library/blob/main/library/convolution/FPS.py
# https://github.com/atcoder/ac-library/blob/master/atcoder/convolution.hpp
from array import array
MOD = 998244353
IMAG = 911660635
IIMAG = 86583718
INV2 = 499122177
rate2 = array('I', [0, 911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899, 0])
irate2 = array('I', [0, 86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235, 0])
rate3 = array('I', [0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0])
irate3 = array('I', [0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0])
# https://judge.yosupo.jp/submission/55648
def butterfly(a: list):
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) % MOD
a[i + offset + p] = (l - r) % MOD
rot *= rate2[(~s & -~s).bit_length()]
rot %= MOD
le += 1
else:
p = 1 << (h - le - 2)
rot = 1
for s in range(1 << le):
rot2 = rot * rot % MOD
rot3 = rot2 * rot % 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) % MOD * IMAG
a[i + offset] = (a0 + a2 + a1 + a3) % MOD
a[i + offset + p] = (a0 + a2 - a1 - a3) % MOD
a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD
a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD
rot *= rate3[(~s & -~s).bit_length()]
rot %= MOD
le += 2
def butterfly_inv(a: list):
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) % MOD
a[i + offset + p] = (l - r) * irot % MOD
irot *= irate2[(~s & -~s).bit_length()]
irot %= MOD
le -= 1
else:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 2)):
irot2 = irot * irot % MOD
irot3 = irot2 * irot % 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) * IIMAG % MOD
a[i + offset] = (a0 + a1 + a2 + a3) % MOD
a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD
a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD
a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD
irot *= irate3[(~s & -~s).bit_length()]
irot %= MOD
le -= 2
def intt(a):
if len(a) <= 1: return
butterfly_inv(a)
iv = pow(len(a), MOD - 2, MOD)
for i, x in enumerate(a): a[i] = x * iv % MOD
def multiply(s: list, t: list):
n = len(s)
m = len(t)
if min(n, m) <= 60:
a = [0] * (n + m - 1)
for i in range(n):
if i&0b111 == 0:
for j in range(m):
a[i + j] += s[i] * t[j]
a[i + j] %= MOD
else:
for j in range(m):
a[i + j] += s[i] * t[j]
return [x % MOD for x in a]
a = s.copy()
b = t.copy()
z = 1 << (n + m - 2).bit_length()
a += [0] * (z - n)
b += [0] * (z - m)
butterfly(a)
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)
return [v * iz % MOD for v in a]
def pow2(s: list):
n = len(s)
l = (n << 1) - 1
if n <= 60:
a = [0] * l
for i, x in enumerate(s):
for j, y in enumerate(s):
a[i + j] += x * y
return [x % MOD for x in a]
z = 1 << (l - 1).bit_length()
a = s + [0] * (z - n)
butterfly(a)
for i, x in enumerate(a): a[i] = x * x % MOD
butterfly_inv(a)
a[l:] = []
iz = pow(z, MOD - 2, MOD)
return [x * iz % MOD for x in a]
def shrink(a: list):
while a and not a[-1]: a.pop()
def fps_add(a: list, b: list):
if len(a) < len(b):
res = b.copy()
for i, x in enumerate(a):
res[i] += x
else:
res = a.copy()
for i, x in enumerate(b):
res[i] += x
return [x-MOD if MOD <= x else x for x in res]
def fps_sub(a: list, b: list):
if len(a) < len(b):
res = b.copy()
for i, x in enumerate(a):
res[i] -= x
return [MOD-x if 0 < x else -x for x in res]
else:
res = a.copy()
for i, x in enumerate(b):
res[i] -= x
return [x if 0 <= x else x+MOD for x in res]
def fps_neg(a: list):
return [MOD-x if x else 0 for x in a]
def fps_div(a: list, b: list) -> list:
if len(a) < len(b): return []
n = len(a) - len(b) + 1
cnt = 0
if len(b) > 64:
return multiply(a[::-1][:n], fps_inv(b[::-1], n))[:n][::-1]
f = a.copy()
g = b.copy()
while g and not g[-1]:
g.pop()
cnt += 1
coef = pow(g[-1], MOD - 2, MOD)
g = [x * coef % MOD for x in g]
deg = len(f) - len(g) + 1
lg = len(g)
res = [0] * deg
for i in reversed(range(deg)):
res[i] = x = f[i + lg - 1] % MOD
for j, y in enumerate(g):
f[i + j] -= x * y
return [x * coef % MOD for x in res] + [0] * cnt
def fps_mod(a: list, b: list) -> list:
res = fps_sub(a, multiply(fps_div(a, b), b))
while res and not res[-1]: res.pop()
return res
def fps_divmod(a: list, b: list):
q = fps_div(a, b)
r = fps_sub(a, multiply(q, b))
while r and not r[-1]: r.pop()
return q, r
def fps_eval(a: list, x: int) -> int:
r = 0
w = 1
for v in a:
r += w * v % MOD
w = w * x % MOD
return r % MOD
def fps_inv(a: list, deg: int=-1):
# assert(self[0] != 0)
if deg == -1: deg = len(a)
res = [0] * deg
res[0] = pow(a[0], MOD - 2, MOD)
d = 1
iv = INV2
while d < deg:
d2 = d << 1
f = [0] * d2
fl = min(len(a), d2)
f[:fl] = a[:fl]
g = [0] * d2
g[:d] = res[:d]
butterfly(g)
butterfly(f)
for i in range(d2): f[i] = f[i] * g[i] % MOD
butterfly_inv(f)
f[:d] = [0] * d
for i in range(d, d2): f[i] = f[i] * iv % MOD
butterfly(f)
for i in range(d2): f[i] = f[i] * g[i] % MOD
butterfly_inv(f)
for i in range(d, min(d2, deg)): res[i] = (MOD-f[i]) * iv % MOD
d <<= 1
iv = iv * INV2 % MOD
return res
def fps_pow(a: list, k: int, deg=-1) -> list:
n = len(a)
if deg == -1: deg = n
if k == 0:
if not deg: return []
res = [0] * deg
res[0] = 1
return res
for i, x in enumerate(a):
if x:
iz = pow(x, MOD - 2, MOD)
res = [x * iz % MOD for x in a[i:]]
res = fps_log(res, deg)
res = [x * k % MOD for x in res]
res = fps_exp(res, deg)
coef = pow(x, k, MOD)
res = [0] * (i * k) + [x * coef % MOD for x in res]
if len(res) < deg:
return res + [0] * (deg - len(res))
return res[:deg]
if (i + 1) * k >= deg: break
return [0] * deg
def fps_exp(a: list, deg: int=-1):
# assert a[0] == 0
if deg == -1: deg = len(a)
inv = [0, 1]
def inplace_integral(f: list) -> list:
n = len(f)
while len(inv) <= n:
j, k = divmod(MOD, len(inv))
inv.append((-inv[k] * j) % MOD)
return [0] + [x * inv[i + 1] % MOD for i, x in enumerate(f)]
b = [1, (a[1] if 1 < len(a) else 0)]
c = [1]
z1 = []
z2 = [1, 1]
m = 2
while m < deg:
y = b + [0] * m
butterfly(y)
z1 = z2
z = [y[i] * p % MOD for i, p in enumerate(z1)]
intt(z)
z[:m >> 1] = [0] * (m >> 1)
butterfly(z)
for i, p in enumerate(z1): z[i] = z[i] * (-p) % MOD
intt(z)
c[m >> 1:] = z[m >> 1:]
z2 = c + [0] * m
butterfly(z2)
tmp = min(len(a), m)
x = a[:tmp] + [0] * (m - tmp)
x = fps_diff(x)
x.append(0)
butterfly(x)
for i, p in enumerate(x): x[i] = y[i] * p % MOD
intt(x)
for i, p in enumerate(b):
if not i: continue
x[i - 1] -= p * i % MOD
x += [0] * m
for i in range(m - 1): x[m + i], x[i] = x[i], 0
butterfly(x)
for i, p in enumerate(z2): x[i] = x[i] * p % MOD
intt(x)
x.pop()
x = inplace_integral(x)
x[:m] = [0] * m
for i in range(m, min(len(a), m << 1)): x[i] += a[i]
butterfly(x)
for i, p in enumerate(y): x[i] = x[i] * p % MOD
intt(x)
b[m:] = x[m:]
m <<= 1
return b[:deg]
def fps_log(a: list, deg=-1) -> list:
# assert(a[0] == 1)
if deg == -1: deg = len(a)
return fps_integral(multiply(fps_diff(a), fps_inv(a, deg))[:deg - 1])
def fps_integral(a: list):
n = len(a)
res = [0] * (n + 1)
if n: res[1] = 1
for i in range(2, n + 1):
j, k = divmod(MOD, i)
res[i] = (-res[k] * j) % MOD
for i, x in enumerate(a): res[i + 1] = res[i + 1] * x % MOD
return res
def fps_diff(a: list):
return [i * x % MOD for i, x in enumerate(a) if i]
def LinearRecurrence(n: int, p: list, q: list):
"""
[x^n]P(x)/Q(x)
"""
# assert len(p) < len(q)
shrink(q)
while n:
q2 = q[:]
for i in range(1,len(q2),2): q2[i] = (-q2[i])%MOD
s = multiply(p,q2)
t = multiply(q,q2)
p = s[n&1::2]
q = t[0::2]
n >>= 1
return p[0] * pow(q[0], -1, MOD) % MOD
def fps_compsite(f: list, g: list):
"""
g(f(x)) mod x^(n+1)
"""
# assert len(f) == len(g)
def trans_multiply(s, t):
n = len(s)
m = len(t)
l = 1 << (max(n, m) - 1).bit_length()
a = s + [0] * (l - n)
b = t + [0] * (l - m)
a = [a[0]] + [a[l - i] for i in range(1, l)]
butterfly(a)
butterfly(b)
iz = pow(l, MOD-2, MOD)
for i, x in enumerate(b):
a[i] = a[i] * x % MOD * iz % MOD
butterfly_inv(a)
a = [a[0]] + [a[l - i] for i in range(1, l)]
return a[:n - m + 1]
n = len(f)
l = 1 << (n - 1).bit_length()
a = [MOD - x for x in f] + [0] * (2 * l - n)
b = g + [0] * (l - n)
def _inner(q, n, k):
if n == 1:
p = [0] * (2 * k)
p[0::2] = b[::-1]
return p
siz = 2 * n * k
r = [MOD - x if i & 1 else x for i,x in enumerate(q)]
qq = multiply(q, r)
qq.append(0)
for i in range(0, siz, 2):
qq[siz+i] = (qq[siz+i] + 2 * q[i]) % MOD
nq = [0] * siz
for j in range(2 * k):
for i in range(n >> 1):
nq[n * j + i] = qq[2 * n * j + 2 * i]
np = _inner(nq, n >> 1, k << 1)
pq = [0] * (2 * siz)
for j in range(2 * k):
for i in range(n >> 1):
pq[2 * n * j + 2 * i + 1] = np[n * j + i]
p = [pq[siz + i] for i in range(siz)]
pq.pop()
x = trans_multiply(pq, r)
p = [(p[i] + x[i]) % MOD for i in range(siz)]
return p
p = _inner(a, l, 1)
p = p[l-1::-1]
return p[:n]
# https://atcoder.jp/contests/abc345/submissions/61504515
def power_projection(f, wt, m):
"""
sum_{j = 0}^{j = n - 1}(wt_j * [x^j]f^i) (0 <= i < m)
"""
if len(f) == 0:
return [0 for _ in range(m)]
# f[0] = c のとき f[0] = 0 の問題にする.
if f[0] != 0:
c = f[0]
f[0] = 0
A = power_projection(f, wt, m)
f[0] = c
for p in range(m):
A[p] = A[p] * finv[p] % MOD
B = [0 for _ in range(m)]
Pow = 1
for q in range(m):
B[q] = Pow * finv[q] % MOD
Pow = Pow * c % MOD
A = multiply(A, B)
while len(A) > m:
A.pop()
for i in range(m):
A[i] = A[i] * fact[i] % MOD
return A
n = 1
log = 1
while n < len(f):
n *= 2
log += 1
for i in range(n - len(f)):
f.append(0), wt.append(0)
wt = wt[::-1]
M = 2 * n
btr = [0] * M
for i in range(1, M):
btr[i] = (btr[i >> 1] >> 1) + ((i & 1) << (log - 1))
# W[i] = w_(4 * N) ^ rev(i) in bit-reverse order.
t, r = 23, 31
dw = pow(pow(r, -1, MOD), (1 << t) // (2 * M), MOD) # 4*N = 2*M
W = [0] * M
w = 1
for i in btr:
W[i] = w
w = w * dw % MOD
root_delta = 7516853
inv_root_delta = pow(root_delta, -1, M)
mask = M - 1
inv_2 = (MOD + 1) // 2
mul_w = [0] * M
pair = [0] * M
for i in range(M):
rev_ai = (btr[i] * inv_root_delta) & mask
ai = btr[rev_ai]
j0 = (i << 1) | (((root_delta * rev_ai) >> log) & 1)
pair[i] = j0
mul_w[i] = inv_2 * W[ai] % MOD
k = 1
P, Q = [0 for _ in range(2 * n)], [0 for _ in range(2 * n)]
for i in range(n):
P[i], Q[i] = wt[i], (-f[i]) % MOD
# https://noshi91.hatenablog.com/entry/2023/12/10/163348
while n > 1:
for i in range(2 * n * k):
P.append(0), Q.append(0)
Q[2 * n * k] = 1
# R(x, y) = Q(-x, y) の fft は Q(x, y)から分かる.
butterfly(P)
butterfly(Q)
# f(x) = e(x^2) + x * o(x^2) のとき fft(e), fft(o) は fft(f) から分かる.
for i in range(M):
j = pair[i]
P[i] = (P[j] * Q[j^1] - P[j^1] * Q[j]) % MOD
P[i] = P[i] * mul_w[i] % MOD
Q[i] = Q[j] * Q[j^1] % MOD
for i in range(2 * n * k):
P.pop(), Q.pop()
intt(P)
intt(Q)
# x の次数を半分に
for j in range(2 * k):
for i in range(n // 2, n):
P[n * j + i], Q[n * j + i] = 0, 0
Q[0] = 0
n, k = n // 2, k * 2
p = [0 for i in range(k)]
for i in range(k):
p[i] = P[2 * i]
p = p[::-1]
for i in range(m - len(p)):
p.append(0)
while len(p) > m:
p.pop()
return p
def fps_compsite_inv(f):
n = len(f) - 1
# assert f[0] % MOD == 0
if n == 0: return f
# assert f[1] % MOD != 0
iz = pow(f[1], MOD-2, MOD)
nf = [x*iz%MOD for x in f]
wt = [0] * n + [1]
a = power_projection(nf, wt, n + 1)
# print(a, n)
g = [0] + fps_pow([n*a[n-i]%MOD*pow(n-i,MOD-2,MOD)%MOD for i in range(n)], MOD-pow(n, MOD-2, MOD))
p = 1
for i in range(len(g)):
g[i] = g[i] * p % MOD
p = p * iz % MOD
return g
# ?
# def fps_compsitional_inv(calc, deg):
# """
# input
# calc(g, d) = f(g(x)) mod x^d を計算する
# fps_compsite よりも良い計算量のものが存在するならば書く
# output
# g(x) mod x^deg s.t. f(g(x)) = x
# """
# c = deg.bit_length()
# g = calc([0, 1], 2)
# g[1] = pow(g[1], -1, MOD)
# d = 2
# for i in range(c):
# d <<= 1
# fg = calc(g, d)
# fdg = multiply(fps_diff(fg), fps_inv(fps_diff(g)))
# fdg[d:] = []
# fg[1] -= 1
# g = fps_sub(g, multiply(fg, fps_inv(fdg)))
# g[d:] = []
# g[deg:] = []
# return g
INVMOD = [1,1]
def SubsetSum(d: list) -> list:
"""
\prod ( 1 + x^i ) ^ d[i]
d[w] = 重さ w が d[w] 種類 1 個ずつある
r[w] = 重さが w になるような選び方
"""
n = len(d)
for i in range(len(INVMOD), n):
INVMOD.append(-INVMOD[MOD%i] * (MOD//i) % MOD)
res = [0] * n
sgn = [-1, 1]
for i in range(1, n):
if d[i]:
tmp = d[i] * i
for j in range(i, n, i):
res[j] += tmp * INVMOD[j] * sgn[(j//i)&1] % MOD
res = fps_exp(res, n)
return res
def MultisetSum(d: list) -> list:
"""
\prod ( 1 / ( 1 - x^i ) ) ^ d[i]
d[w] = 重さ w が d[w] 種類 inf 個ずつある
r[w] = 重さが w になるような選び方
"""
n = len(d)
for i in range(len(INVMOD), n):
INVMOD.append(-INVMOD[MOD%i] * (MOD//i) % MOD)
res = [0] * n
for i in range(1, n):
if d[i]:
tmp = d[i] * i
for j in range(i, n, i):
res[j] += tmp * INVMOD[j] % MOD
res = fps_exp(res, n)
return res
fac = [1, 1]
finv = [1, 1]
def tayler_shift(a: list, c: int) -> list:
global fac, finv
n = len(a)
l = len(fac)
fac += [0] * (n - l)
finv += [0] * (n - l)
for i in range(l, n):
fac[i] = fac[i-1] * i % MOD
finv[n-1] = pow(fac[n-1], MOD-2, MOD)
for i in reversed(range(l, n-1)):
finv[i] = finv[i+1] * (i+1) % MOD
r = [x * fac[i] % MOD for i, x in enumerate(a)]
b = [0] * n
b[0] = 1
for i in range(1, n):
b[i] = b[i-1] * c % MOD * finv[i] % MOD * fac[i-1] % MOD
r.reverse()
res = multiply(r, b)[:n]
return [x * finv[i] % MOD for i, x in enumerate(reversed(res))]
def fps_product(polys):
if len(polys) == 0:
return [1]
from collections import deque
que = deque(polys)
while len(que) > 1:
que.append(multiply(que.popleft(), que.popleft()))
return que[0]
def ntt2d(a: list[list]):
n, m = len(a), len(a[0])
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):
for j in range(m):
l = a[i + offset][j]
r = a[i + offset + p][j] * rot
a[i + offset][j] = (l + r) % MOD
a[i + offset + p][j] = (l - r) % MOD
rot *= rate2[(~s & -~s).bit_length()]
rot %= MOD
le += 1
else:
p = 1 << (h - le - 2)
rot = 1
for s in range(1 << le):
rot2 = rot * rot % MOD
rot3 = rot2 * rot % MOD
offset = s << (h - le)
for i in range(p):
for j in range(m):
a0 = a[i + offset][j]
a1 = a[i + offset + p][j] * rot
a2 = a[i + offset + p * 2][j] * rot2
a3 = a[i + offset + p * 3][j] * rot3
a1na3imag = (a1 - a3) % MOD * IMAG
a[i + offset][j] = (a0 + a2 + a1 + a3) % MOD
a[i + offset + p][j] = (a0 + a2 - a1 - a3) % MOD
a[i + offset + p * 2][j] = (a0 - a2 + a1na3imag) % MOD
a[i + offset + p * 3][j] = (a0 - a2 - a1na3imag) % MOD
rot *= rate3[(~s & -~s).bit_length()]
rot %= MOD
le += 2
n, m = m, n
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):
for j in range(m):
l = a[j][i + offset]
r = a[j][i + offset + p] * rot
a[j][i + offset] = (l + r) % MOD
a[j][i + offset + p] = (l - r) % MOD
rot *= rate2[(~s & -~s).bit_length()]
rot %= MOD
le += 1
else:
p = 1 << (h - le - 2)
rot = 1
for s in range(1 << le):
rot2 = rot * rot % MOD
rot3 = rot2 * rot % MOD
offset = s << (h - le)
for i in range(p):
for j in range(m):
a0 = a[j][i + offset]
a1 = a[j][i + offset + p] * rot
a2 = a[j][i + offset + p * 2] * rot2
a3 = a[j][i + offset + p * 3] * rot3
a1na3imag = (a1 - a3) % MOD * IMAG
a[j][i + offset] = (a0 + a2 + a1 + a3) % MOD
a[j][i + offset + p] = (a0 + a2 - a1 - a3) % MOD
a[j][i + offset + p * 2] = (a0 - a2 + a1na3imag) % MOD
a[j][i + offset + p * 3] = (a0 - a2 - a1na3imag) % MOD
rot *= rate3[(~s & -~s).bit_length()]
rot %= MOD
le += 2
def intt2d(a : list[list]):
n, m = len(a), len(a[0])
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):
for j in range(m):
l = a[i + offset][j]
r = a[i + offset + p][j]
a[i + offset][j] = (l + r) % MOD
a[i + offset + p][j] = (l - r) * irot % MOD
irot *= irate2[(~s & -~s).bit_length()]
irot %= MOD
le -= 1
else:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 2)):
irot2 = irot * irot % MOD
irot3 = irot2 * irot % MOD
offset = s << (h - le + 2)
for i in range(p):
for j in range(m):
a0 = a[i + offset][j]
a1 = a[i + offset + p][j]
a2 = a[i + offset + p * 2][j]
a3 = a[i + offset + p * 3][j]
a2na3iimag = (a2 - a3) * IIMAG % MOD
a[i + offset][j] = (a0 + a1 + a2 + a3) % MOD
a[i + offset + p][j] = (a0 - a1 + a2na3iimag) * irot % MOD
a[i + offset + p * 2][j] = (a0 + a1 - a2 - a3) * irot2 % MOD
a[i + offset + p * 3][j] = (a0 - a1 - a2na3iimag) * irot3 % MOD
irot *= irate3[(~s & -~s).bit_length()]
irot %= MOD
le -= 2
n, m = m, n
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):
for j in range(m):
l = a[j][i + offset]
r = a[j][i + offset + p]
a[j][i + offset] = (l + r) % MOD
a[j][i + offset + p] = (l - r) * irot % MOD
irot *= irate2[(~s & -~s).bit_length()]
irot %= MOD
le -= 1
else:
p = 1 << (h - le)
irot = 1
for s in range(1 << (le - 2)):
irot2 = irot * irot % MOD
irot3 = irot2 * irot % MOD
offset = s << (h - le + 2)
for i in range(p):
for j in range(m):
a0 = a[j][i + offset]
a1 = a[j][i + offset + p]
a2 = a[j][i + offset + p * 2]
a3 = a[j][i + offset + p * 3]
a2na3iimag = (a2 - a3) * IIMAG % MOD
a[j][i + offset] = (a0 + a1 + a2 + a3) % MOD
a[j][i + offset + p] = (a0 - a1 + a2na3iimag) * irot % MOD
a[j][i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % MOD
a[j][i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % MOD
irot *= irate3[(~s & -~s).bit_length()]
irot %= MOD
le -= 2
iv = pow(n * m, MOD - 2, MOD)
for i in range(m):
for j in range(n):
a[i][j] = a[i][j] * iv % MOD
def multiply2d(s: list[list], t: list[list]):
"""
not verify
"""
from copy import deepcopy
hs, ws = len(s), len(s[0])
ht, wt = len(t), len(t[0])
h = 1 << (hs + ht - 2).bit_length()
w = 1 << (ws + wt - 2).bit_length()
a = deepcopy(s)
b = deepcopy(t)
for i in range(hs):
a[i] += [0] * (w - ws)
for i in range(ht):
b[i] += [0] * (w - wt)
a += [[0]*w for i in range(h - hs)]
b += [[0]*w for i in range(h - ht)]
intt2d(a)
intt2d(b)
for i in range(h):
for j in range(w):
a[i][j] *= b[i][j]
a[i][j] %= MOD
intt2d(a)
a = a[:hs + ht - 1]
for i in range(hs + ht - 1):
a[i][ws + wt - 1:] = []
return a
n, m = list(map(int,input().split()))
a = list(map(int,input().split()))
b = list(map(int,input().split()))
c = list(map(int,input().split()))
import sys
sys.setrecursionlimit(10**7)
import pypyjit
pypyjit.set_param('max_unroll_recursion=-1')
now = 1
f = a
ans = [0] * len(a)
ans[1] = 1 # x
while now <= m:
if now&m:
ans = fps_compsite(ans, f)
if now * 2 <= m:
f = fps_compsite(f, f)
now <<= 1
print(*ans)
# # 行列累乗的な？
# from functools import cache
# @cache
# def compsite_pow(f, m):
# if m == 0:
# return fps_pow(f, 0)
# elif m == 1:
# return fps_pow(f, 1)
# elif m % 2 == 0:
# return compsite_pow(fps_compsite(f, f), m // 2)
# else:
# return fps_compsite(f, compsite_pow(f, m-1))
# print(*compsite_pow(a, m))