結果
| 問題 |
No.829 成長関数インフレ中
|
| コンテスト | |
| ユーザー |
 vwxyz
|
| 提出日時 | 2024-04-14 08:37:57 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 6,190 bytes |
| コンパイル時間 | 166 ms |
| コンパイル使用メモリ | 82,232 KB |
| 実行使用メモリ | 278,396 KB |
| 最終ジャッジ日時 | 2024-10-03 05:44:35 |
| 合計ジャッジ時間 | 6,870 ms |
|
ジャッジサーバーID （参考情報） |
judge5 / judge2 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 15 TLE * 2 -- * 5 |
ソースコード
from collections import deque
import math
def Extended_Euclid(n,m):
stack=[]
while m:
stack.append((n,m))
n,m=m,n%m
if n>=0:
x,y=1,0
else:
x,y=-1,0
for i in range(len(stack)-1,-1,-1):
n,m=stack[i]
x,y=y,x-(n//m)*y
return x,y
class MOD:
def __init__(self,p,e=None):
self.p=p
self.e=e
if self.e==None:
self.mod=self.p
else:
self.mod=self.p**self.e
def Pow(self,a,n):
a%=self.mod
if n>=0:
return pow(a,n,self.mod)
else:
#assert math.gcd(a,self.mod)==1
x=Extended_Euclid(a,self.mod)[0]
return pow(x,-n,self.mod)
def Build_Fact(self,N):
assert N>=0
self.factorial=[1]
if self.e==None:
for i in range(1,N+1):
self.factorial.append(self.factorial[-1]*i%self.mod)
else:
self.cnt=[0]*(N+1)
for i in range(1,N+1):
self.cnt[i]=self.cnt[i-1]
ii=i
while ii%self.p==0:
ii//=self.p
self.cnt[i]+=1
self.factorial.append(self.factorial[-1]*ii%self.mod)
self.factorial_inve=[None]*(N+1)
self.factorial_inve[-1]=self.Pow(self.factorial[-1],-1)
for i in range(N-1,-1,-1):
ii=i+1
while ii%self.p==0:
ii//=self.p
self.factorial_inve[i]=(self.factorial_inve[i+1]*ii)%self.mod
def Build_Inverse(self,N):
self.inverse=[None]*(N+1)
assert self.p>N
self.inverse[1]=1
for n in range(2,N+1):
if n%self.p==0:
continue
a,b=divmod(self.mod,n)
self.inverse[n]=(-a*self.inverse[b])%self.mod
def Inverse(self,n):
return self.inverse[n]
def Fact(self,N):
if N<0:
return 0
retu=self.factorial[N]
if self.e!=None and self.cnt[N]:
retu*=pow(self.p,self.cnt[N],self.mod)%self.mod
retu%=self.mod
return retu
def Fact_Inve(self,N):
if self.e!=None and self.cnt[N]:
return None
return self.factorial_inve[N]
def Comb(self,N,K,divisible_count=False):
if K<0 or K>N:
return 0
retu=self.factorial[N]*self.factorial_inve[K]%self.mod*self.factorial_inve[N-K]%self.mod
if self.e!=None:
cnt=self.cnt[N]-self.cnt[N-K]-self.cnt[K]
if divisible_count:
return retu,cnt
else:
retu*=pow(self.p,cnt,self.mod)
retu%=self.mod
return retu
def FFT(polynomial0,polynomial1,digit=10**5,round_to_int=True):
assert digit==0 or round_to_int
if len(polynomial0)*len(polynomial1)<=60:
polynomial=[0]*(len(polynomial0)+len(polynomial1)-1)
for i in range(len(polynomial0)):
for j in range(len(polynomial1)):
polynomial[i+j]+=polynomial0[i]*polynomial1[j]
return polynomial
def DFT(polynomial,n,inverse=False):
if inverse:
primitive_root=[math.cos(-i*2*math.pi/(1<<n))+math.sin(-i*2*math.pi/(1<<n))*1j for i in range(1<<n)]
else:
primitive_root=[math.cos(i*2*math.pi/(1<<n))+math.sin(i*2*math.pi/(1<<n))*1j for i in range(1<<n)]
if inverse:
for bit in range(1,n+1):
a=1<<bit-1
for i in range(1<<n-bit):
for j in range(a):
s=i*2*a+j
t=s+a
polynomial[s],polynomial[t]=polynomial[s]+polynomial[t]*primitive_root[j<<n-bit],polynomial[s]-polynomial[t]*primitive_root[j<<n-bit]
else:
for bit in range(n,0,-1):
a=1<<bit-1
for i in range(1<<n-bit):
for j in range(a):
s=i*2*a+j
t=s+a
polynomial[s],polynomial[t]=polynomial[s]+polynomial[t],primitive_root[j<<n-bit]*(polynomial[s]-polynomial[t])
def FFT_(polynomial0,polynomial1,round_to_int=True):
N0=len(polynomial0)
N1=len(polynomial1)
N=N0+N1-1
n=(N-1).bit_length()
polynomial0=polynomial0+[0]*((1<<n)-N0)
polynomial1=polynomial1+[0]*((1<<n)-N1)
DFT(polynomial0,n)
DFT(polynomial1,n)
fft=[x*y for x,y in zip(polynomial0,polynomial1)]
DFT(fft,n,inverse=True)
if round_to_int:
fft=[round((fft[i]/(1<<n)).real) for i in range(N)]
else:
fft=[(fft[i]/(1<<n)).real for i in range(N)]
return fft
if digit:
N0=len(polynomial0)
N1=len(polynomial1)
N=N0+N1-1
polynomial00,polynomial01=[None]*N0,[None]*N0
polynomial10,polynomial11=[None]*N1,[None]*N1
for i in range(N0):
polynomial00[i],polynomial01[i]=divmod(polynomial0[i],digit)
for i in range(N1):
polynomial10[i],polynomial11[i]=divmod(polynomial1[i],digit)
polynomial=[0]*N
for i,x in enumerate(FFT_(polynomial00,polynomial10)):
polynomial[i]+=x*(digit**2-digit)
for i,x in enumerate(FFT_(polynomial01,polynomial11)):
polynomial[i]-=x*(digit-1)
for i,x in enumerate(FFT_([x1+x2 for x1,x2 in zip(polynomial00,polynomial01)],[x1+x2 for x1,x2 in zip(polynomial10,polynomial11)])):
polynomial[i]+=x*digit
else:
polynomial=FFT_(polynomial0,polynomial1,round_to_int=round_to_int)
return polynomial
N,B=map(int,input().split())
mod=10**9+7
MD=MOD(mod)
MD.Build_Fact(N)
C=[0]*N
for s in map(int,input().split()):
C[s]+=1
cnt=0
queue=[]
for s in range(N-1,-1,-1):
if C[s]:
if queue:
c=MD.Fact(cnt+C[s]-1)*MD.Fact_Inve(cnt)%mod
queue.append([c*cnt%mod,c*C[s]%mod])
else:
queue.append([0,MD.Fact(C[s])])
cnt+=C[s]
queue=deque(queue)
while len(queue)>=2:
queue.append([x%mod for x in FFT(queue.popleft(),queue.popleft())])
ans=sum(c*s*pow(B,s,mod)for s,c in enumerate(queue[0]))%mod
print(ans)