結果

問題 No.2966 Simple Plus Minus Problem
ユーザー PNJ
提出日時 2024-11-16 17:59:42
言語 PyPy3
(7.3.15)
結果
RE  
実行時間 -
コード長 5,601 bytes
コンパイル時間 600 ms
コンパイル使用メモリ 82,268 KB
実行使用メモリ 129,812 KB
最終ジャッジ日時 2024-11-16 17:59:55
合計ジャッジ時間 10,887 ms
ジャッジサーバーID
(参考情報)
judge1 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 32 RE * 22
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ソースコード

diff #
プレゼンテーションモードにする

mod = 998244353
n = 300000
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
def binom(n,r):
if n < r or n < 0 or r < 0:
return 0
res = fact_inv[n - r] * fact_inv[r] % mod
res *= fact[n]
res %= mod
return res
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 = pow(n,mod - 2,mod)
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) <= 60:
return convolute_naive(s,t)
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
N,K = map(int,input().split())
A = list(map(int,input().split()))
f = [0 for i in range(N)]
f[0] = 1
for i in range(2,N,2):
j = i // 2
f[i] = binom(j + K // 2 - 1,j)
f = convolute(f,A)[:N]
if K % 2:
for i in range(N):
if i % 2:
f[i] = mod - f[i]
for i in range(N - 1):
f[i + 1] += f[i]
f[i + 1] %= mod
print(*f)
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