結果
| 問題 | No.2763 Macaron Gift Box |
| ユーザー |
 PNJ
|
| 提出日時 | 2024-07-14 01:53:42 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,076 ms / 3,000 ms |
| コード長 | 8,946 bytes |
| コンパイル時間 | 595 ms |
| コンパイル使用メモリ | 82,132 KB |
| 実行使用メモリ | 127,664 KB |
| 最終ジャッジ日時 | 2024-07-14 01:53:55 |
| 合計ジャッジ時間 | 9,684 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge5 |
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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 | 78 ms
69,216 KB |
| testcase_01 | AC | 80 ms
69,008 KB |
| testcase_02 | AC | 79 ms
69,184 KB |
| testcase_03 | AC | 80 ms
68,748 KB |
| testcase_04 | AC | 78 ms
69,316 KB |
| testcase_05 | AC | 82 ms
69,752 KB |
| testcase_06 | AC | 108 ms
68,684 KB |
| testcase_07 | AC | 591 ms
103,884 KB |
| testcase_08 | AC | 244 ms
89,004 KB |
| testcase_09 | AC | 379 ms
93,572 KB |
| testcase_10 | AC | 1,019 ms
123,964 KB |
| testcase_11 | AC | 1,032 ms
123,812 KB |
| testcase_12 | AC | 1,076 ms
126,936 KB |
| testcase_13 | AC | 1,055 ms
127,664 KB |
| testcase_14 | AC | 247 ms
88,888 KB |
| testcase_15 | AC | 274 ms
89,112 KB |
| testcase_16 | AC | 247 ms
89,136 KB |
ソースコード
mod = 998244353
imag = 911660635
iimag = 86583718
rate2 = (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 = (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 = (0, 372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099, 183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204, 0)
irate3 = (0, 509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681, 0)
def fft(a):
n = len(a)
h = (n - 1).bit_length()
le = 0
while le < h:
if h == le + 1:
p = 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 fft_inv(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) % 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 ntt(a):
if len(a) <= 1:
return
fft(a)
def ntt_inv(a):
if len(a) <= 1:
return
fft_inv(a)
iv = pow(len(a),mod-2,mod)
for i in range(len(a)):
a[i] = a[i] * iv % mod
def convolute(a,b):
aa = a[:]
bb = b[:]
n = len(aa)
m = len(bb)
z = 1 << (n + m - 2).bit_length()
aa += [0] * (z - n)
bb += [0] * (z - m)
fft(aa)
fft(bb)
for i in range(z):
aa[i] = aa[i] * bb[i] % mod
fft_inv(aa)
aa = aa[:n + m - 1]
iz = pow(z, mod - 2, mod)
for i in range(n+m-1):
aa[i] = (aa[i] * iz) % mod
return aa
def fps_inv(f,deg = -1):
assert (f[0] != 0)
if deg == -1:
deg = len(f)
res = [0] * deg
res[0] = pow(f[0],mod-2,mod)
d = 1
while d < deg:
a = [0] * (d << 1)
tmp = min(len(f),d << 1)
a[:tmp] = f[:tmp]
b = [0] * (d << 1)
b[:d] = res[:d]
ntt(a)
ntt(b)
for i in range(d << 1):
a[i] = a[i] * b[i] % mod
ntt_inv(a)
a[:d] = [0] * d
ntt(a)
for i in range(d << 1):
a[i] = a[i] * b[i] % mod
ntt_inv(a)
for j in range(d,min(d << 1,deg)):
if a[j]:
res[j] = mod - a[j]
else:
res[j] = 0
d <<= 1
return res
def fps_div(f,g):
n,m = len(f),len(g)
if n < m:
return [],f
rev_f = f[:]
rev_f = rev_f[::-1]
rev_g = g[:]
rev_g = rev_g[::-1]
rev_q = convolute(rev_f,fps_inv(rev_g,n-m+1))[:n-m+1]
q = rev_q[:]
q = q[::-1]
p = convolute(g,q)
r = f[:]
for i in range(min(len(p),len(r))):
r[i] -= p[i]
r[i] %= mod
while len(r):
if r[-1] != 0:
break
r.pop()
return q,r
def fps_diff(f):
res = []
for i in range(1,len(f)):
res.append(i * f[i] % mod)
return res
def fps_integrate(f):
n = len(f)
res = [0] * (n + 1)
for i in range(n):
res[i+1] = pow(i + 1,mod-2,mod) * f[i] % mod
return res
def fps_log(f,deg = -1):
assert (f[0] != 0)
if deg == -1:
deg = len(f)
c = f[0]
if c != 1:
cc = pow(c,mod - 2,mod)
for i in range(len(f)):
f[i] = f[i] * cc % mod
res = convolute(fps_diff(f),fps_inv(f,deg))
res = fps_integrate(res)
if c != 1:
for i in range(deg):
f[i] = f[i] * c % mod
return res[:deg]
def fps_exp(f,deg = -1):
assert (f[0] == 0)
if deg == -1:
deg = len(f)
res = [1,0]
if len(f) > 1:
res[1] = f[1]
g = [1]
p = []
q = [1,1]
m = 2
while m < deg:
y = res + [0]*m
ntt(y)
p = q[:]
z = [y[i] * p[i] for i in range(len(p))]
ntt_inv(z)
z[:m >> 1] = [0] * (m >> 1)
ntt(z)
for i in range(len(p)):
z[i] = z[i] * (-p[i]) % mod
ntt_inv(z)
g[m >> 1:] = z[m >> 1:]
q = g + [0] * m
ntt(q)
tmp = min(len(f),m)
x = f[:tmp] + [0] * (m - tmp)
x = fps_diff(x)
x.append(0)
ntt(x)
for i in range(len(x)):
x[i] = x[i] * y[i] % mod
ntt_inv(x)
for i in range(len(res)):
if i == 0:
continue
x[i-1] -= res[i] * i % mod
x += [0] * m
for i in range(m-1):
x[m+i],x[i] = x[i],0
ntt(x)
for i in range(len(q)):
x[i] = x[i] * q[i] % mod
ntt_inv(x)
x.pop()
x = fps_integrate(x)
x[:m] = [0] * m
for i in range(m,min(len(f),m << 1)):
x[i] += f[i]
ntt(x)
for i in range(len(y)):
x[i] = x[i] * y[i] % mod
ntt_inv(x)
res[m:] = x[m:]
m <<= 1
return res[:deg]
def fps_pow(f,k,deg = -1):
if k == 0:
return [1] + [0] * (len(f) - 1)
p = 0
if deg == -1:
deg = len(f)
while p < deg:
if f[p]:
break
p += 1
if p == deg:
return [0] * len(f)
a = f[p]
a_inv = pow(a,mod-2,mod)
a = pow(a,k,mod)
f = f[p:]
for i in range(deg-p):
f[i] = f[i] * a_inv % mod
g = fps_log(f,deg)
for i in range(deg-p):
g[i] = g[i] * k % mod
g = fps_exp(g,deg)
res = [0] * deg
for i in range(deg):
j = i + p*k
if j >= deg:
break
res[j] = g[i] * a % mod
return res
n = 10**6
inv = [1 for j in range(n+1)]
for a in range(2,n+1):
# ax + py = 1 <=> rx + p(-x-qy) = -q => x = -(inv[r]) * (p//a) (r = p % a)
res = (mod - inv[mod%a]) * (mod // a)
inv[a] = res % mod
N,K = map(int,input().split())
L = [0 for i in range(N+1)]
for i in range(1,N+1):
for j in range(1,N+1):
if i*j > N:
break
L[i*j] += inv[j]
L[i*j] %= mod
k = (K + 1) * i
for j in range(1,N+1):
if k*j > N:
break
L[k*j] -= inv[j]
L[k*j] %= mod
f = fps_exp(L)
print(*f[1:(N+1)])