結果

問題 No.2959 Dolls' Tea Party
ユーザー PNJ
提出日時 2024-11-08 23:55:00
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 2,457 ms / 3,000 ms
コード長 9,011 bytes
コンパイル時間 216 ms
コンパイル使用メモリ 82,176 KB
実行使用メモリ 137,408 KB
最終ジャッジ日時 2024-11-08 23:56:12
合計ジャッジ時間 68,920 ms
ジャッジサーバーID
(参考情報)
judge4 / judge1
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 4
other AC * 33
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

def make_divisors(n):
lower_divisors , upper_divisors = [], []
i = 1
while i*i < n:
if n % i == 0:
lower_divisors.append(i)
if i != n // i:
upper_divisors.append(n//i)
i += 1
if i * i == n:
lower_divisors.append(i)
return lower_divisors + upper_divisors[::-1]
def gcd(a, b):
while a != 0:
b %= a
if b == 0: return a
a %= b
return b
mod = 998244353
n = 10000
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
fact = [1 for i in range(n + 1)]
for i in range(1,n + 1):
fact[i] = fact[i - 1] * i % mod
fact_inv = [1 for i in range(n + 1)]
fact_inv[-1] = pow(fact[-1],mod - 2,mod)
for i in range(n,0,-1):
fact_inv[i - 1] = fact_inv[i] * i % mod
NTT_friend = [120586241,167772161,469762049,754974721,880803841,924844033,943718401,998244353,1045430273,1051721729,1053818881]
NTT_dict = {}
for i in range(len(NTT_friend)):
NTT_dict[NTT_friend[i]] = i
NTT_info = [[20,74066978],[25,17],[26,30],[24,362],[23,211],[21,44009197],[22,663003469],[23,31],[20,363],[20,330],[20,2789]]
def popcount(n):
c = (n&0x5555555555555555) + ((n>>1)&0x5555555555555555)
c = (c&0x3333333333333333) + ((c>>2)&0x3333333333333333)
c = (c&0x0f0f0f0f0f0f0f0f) + ((c>>4)&0x0f0f0f0f0f0f0f0f)
c = (c&0x00ff00ff00ff00ff) + ((c>>8)&0x00ff00ff00ff00ff)
c = (c&0x0000ffff0000ffff) + ((c>>16)&0x0000ffff0000ffff)
c = (c&0x00000000ffffffff) + ((c>>32)&0x00000000ffffffff)
return c
def topbit(n):
h = n.bit_length()
h -= 1
return h
def prepared_fft(mod = 998244353):
rank2 = NTT_info[NTT_dict[mod]][0]
root,iroot = [0] * 30,[0] * 30
rate2,irate2= [0] * 30,[0] * 30
rate3,irate3= [0] * 30,[0] * 30
root[rank2] = NTT_info[NTT_dict[mod]][1]
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,iprod = 1,1
for i in range(rank2-1):
rate2[i] = root[i + 2] * prod % mod
irate2[i] = iroot[i + 2] * iprod % mod
prod = prod * iroot[i + 2] % mod
iprod = iprod * root[i + 2] % mod
prod,iprod = 1,1
for i in range(rank2-2):
rate3[i] = root[i + 3] * prod % mod
irate3[i] = iroot[i + 3] * iprod % mod
prod = prod * iroot[i + 3] % mod
iprod = iprod * root[i + 3] % mod
return root,iroot,rate2,irate2,rate3,irate3
root,iroot,rate2,irate2,rate3,irate3 = prepared_fft()
def ntt(a):
n = len(a)
h = topbit(n)
assert (n == 1 << h)
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 % mod
a[i + offset] = (l + r) % mod
a[i + offset + p] = (l - r) % mod
rot = rot * rate2[topbit(~s & -~s)] % mod
le += 1
else:
p = 1 << (h - le - 2)
rot,imag = 1,root[2]
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 = rot * rate3[topbit(~s & -~s)] % mod
le += 2
def intt(a):
n = len(a)
h = topbit(n)
assert (n == 1 << h)
coef = inv[n]
for i in range(n):
a[i] = a[i] * coef % mod
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 = irot * irate2[topbit(~s & -~s)] % mod
le -= 1
else:
p = 1 << (h - le)
irot,iimag = 1,iroot[2]
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[topbit(~s & -~s)]
irot %= mod
le -= 2
def convolute_naive(a,b):
res = [0] * (len(a) + len(b) - 1)
for i in range(len(a)):
for j in range(len(b)):
res[i + j] = (res[i + j] + a[i] * b[j] % mod) % mod
return res
def convolute(a,b):
s = a[:]
t = b[:]
n = len(s)
m = len(t)
if min(n,m) <= 30:
return convolute_naive(a,b)
le = 1
while le < n + m - 1:
le *= 2
s += [0] * (le - n)
t += [0] * (le - m)
ntt(s)
ntt(t)
for i in range(le):
s[i] = s[i] * t[i] % mod
intt(s)
s = s[:n + m - 1]
return s
def fps_inv(f,deg = -1):
if deg == -1:
deg = len(f)
res = [0] * deg
res[0] = 1
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
intt(a)
a[:d] = [0] * d
ntt(a)
for i in range(d << 1):
a[i] = a[i] * b[i] % mod
intt(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_add(f,g):
n = max(len(f),len(g))
res = [0] * n
for i in range(len(f)):
res[i] = f[i]
for i in range(len(g)):
res[i] = (res[i] + g[i]) % mod
return res
def fps_diff(f):
if len(f) <= 1:
return [0]
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] = inv[i + 1] * f[i] % mod
return res
def fps_log(f,deg = -1):
assert (f[0] == 1)
if deg == -1:
deg = len(f)
res = convolute(fps_diff(f),fps_inv(f,deg))[:deg - 1]
res = fps_integrate(res)
return res
def fps_exp(f,deg = -1):
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))]
intt(z)
z[:m >> 1] = [0] * (m >> 1)
ntt(z)
for i in range(len(p)):
z[i] = z[i] * (-p[i]) % mod
intt(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
intt(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
intt(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
intt(x)
res[m:] = x[m:]
m <<= 1
return res[:deg]
N,K = map(int,input().split())
A = list(map(int,input().split()))
P = [0 for i in range(K + 1)]
for a in A:
P[min(a,K)] += 1
D = make_divisors(K)
M = len(D)
dic = {}
for i in range(M):
dic[D[i]] = i
LOG = [[]]
g = [1]
for i in range(1,K + 1):
g.append(fact_inv[i])
gg = fps_log(g,K + 1)
LOG.append(gg)
C = []
for d in D:
n = K // d
Q = [0 for i in range(n + 1)]
for i in range(1,K + 1):
Q[min(i // d,n)] += P[i]
f = [0 for j in range(n + 1)]
f[1] = sum(Q) - Q[0]
for i in range(1,n):
if Q[i] == 0:
continue
for j in range(i + 1,n + 1):
f[j] = (f[j] + LOG[i][j] * Q[i] % mod) % mod
f = fps_exp(f)
C.append(f[n] * fact[n] % mod)
res = 0
for k in range(1,K + 1):
g = gcd(k,K)
d = K // g
res += C[dic[d]]
res %= mod
res = res * inv[K] % mod
print(res)
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0