Created
July 2, 2021 13:49
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''' | |
FFTライブラリの詳細!! | |
https://github.com/shakayami/ACL-for-python | |
''' | |
class FFT(): | |
def primitive_root_constexpr(self,m): | |
if m==2:return 1 | |
if m==167772161:return 3 | |
if m==469762049:return 3 | |
if m==754974721:return 11 | |
if m==998244353:return 3 | |
divs=[0]*20 | |
divs[0]=2 | |
cnt=1 | |
x=(m-1)//2 | |
while(x%2==0):x//=2 | |
i=3 | |
while(i*i<=x): | |
if (x%i==0): | |
divs[cnt]=i | |
cnt+=1 | |
while(x%i==0): | |
x//=i | |
i+=2 | |
if x>1: | |
divs[cnt]=x | |
cnt+=1 | |
g=2 | |
while(1): | |
ok=True | |
for i in range(cnt): | |
if pow(g,(m-1)//divs[i],m)==1: | |
ok=False | |
break | |
if ok: | |
return g | |
g+=1 | |
def bsf(self,x): | |
res=0 | |
while(x%2==0): | |
res+=1 | |
x//=2 | |
return res | |
butterfly_first=True | |
butterfly_inv_first=True | |
sum_e=[0]*30 | |
sum_ie=[0]*30 | |
def __init__(self,MOD): | |
self.mod=MOD | |
self.g=self.primitive_root_constexpr(self.mod) | |
def butterfly(self,a): | |
n=len(a) | |
h=(n-1).bit_length() | |
if self.butterfly_first: | |
self.butterfly_first=False | |
es=[0]*30 | |
ies=[0]*30 | |
cnt2=self.bsf(self.mod-1) | |
e=pow(self.g,(self.mod-1)>>cnt2,self.mod) | |
ie=pow(e,self.mod-2,self.mod) | |
for i in range(cnt2,1,-1): | |
es[i-2]=e | |
ies[i-2]=ie | |
e=(e*e)%self.mod | |
ie=(ie*ie)%self.mod | |
now=1 | |
for i in range(cnt2-2): | |
self.sum_e[i]=((es[i]*now)%self.mod) | |
now*=ies[i] | |
now%=self.mod | |
for ph in range(1,h+1): | |
w=1<<(ph-1) | |
p=1<<(h-ph) | |
now=1 | |
for s in range(w): | |
offset=s<<(h-ph+1) | |
for i in range(p): | |
l=a[i+offset] | |
r=a[i+offset+p]*now | |
r%=self.mod | |
a[i+offset]=l+r | |
a[i+offset]%=self.mod | |
a[i+offset+p]=l-r | |
a[i+offset+p]%=self.mod | |
now*=self.sum_e[(~s & -~s).bit_length()-1] | |
now%=self.mod | |
def butterfly_inv(self,a): | |
n=len(a) | |
h=(n-1).bit_length() | |
if self.butterfly_inv_first: | |
self.butterfly_inv_first=False | |
es=[0]*30 | |
ies=[0]*30 | |
cnt2=self.bsf(self.mod-1) | |
e=pow(self.g,(self.mod-1)>>cnt2,self.mod) | |
ie=pow(e,self.mod-2,self.mod) | |
for i in range(cnt2,1,-1): | |
es[i-2]=e | |
ies[i-2]=ie | |
e=(e*e)%self.mod | |
ie=(ie*ie)%self.mod | |
now=1 | |
for i in range(cnt2-2): | |
self.sum_ie[i]=((ies[i]*now)%self.mod) | |
now*=es[i] | |
now%=self.mod | |
for ph in range(h,0,-1): | |
w=1<<(ph-1) | |
p=1<<(h-ph) | |
inow=1 | |
for s in range(w): | |
offset=s<<(h-ph+1) | |
for i in range(p): | |
l=a[i+offset] | |
r=a[i+offset+p] | |
a[i+offset]=l+r | |
a[i+offset]%=self.mod | |
a[i+offset+p]=(l-r)*inow | |
a[i+offset+p]%=self.mod | |
inow*=self.sum_ie[(~s & -~s).bit_length()-1] | |
inow%=self.mod | |
def convolution(self,a,b): | |
n=len(a);m=len(b) | |
if not(a) or not(b): | |
return [] | |
if min(n,m)<=40: | |
if n<m: | |
n,m=m,n | |
a,b=b,a | |
res=[0]*(n+m-1) | |
for i in range(n): | |
for j in range(m): | |
res[i+j]+=a[i]*b[j] | |
res[i+j]%=self.mod | |
return res | |
z=1<<((n+m-2).bit_length()) | |
a=a+[0]*(z-n) | |
b=b+[0]*(z-m) | |
self.butterfly(a) | |
self.butterfly(b) | |
c=[0]*z | |
for i in range(z): | |
c[i]=(a[i]*b[i])%self.mod | |
self.butterfly_inv(c) | |
iz=pow(z,self.mod-2,self.mod) | |
for i in range(n+m-1): | |
c[i]=(c[i]*iz)%self.mod | |
return c[:n+m-1] | |
A,B,C,K=map(int,input().split()) | |
X,Y,Z=map(int,input().split()) | |
mod=998244353 | |
MAX_N=200000 | |
Fact=[0 for i in range(MAX_N+1)] | |
Finv=[0 for i in range(MAX_N+1)] | |
Fact[0]=1 | |
for i in range(MAX_N):Fact[i+1]=((i+1)*Fact[i])%mod | |
Finv[MAX_N]=pow(Fact[MAX_N],mod-2,mod) | |
for i in range(MAX_N-1,-1,-1):Finv[i]=((i+1)*Finv[i+1])%mod | |
def binomial(n,k): | |
if 0<=k<=n: | |
return Fact[n]*Finv[k]%mod*Finv[n-k]%mod | |
else: | |
return 0 | |
P=[binomial(A,K-i) for i in range(Y+1)] | |
Q=[binomial(B,K-j) for j in range(Z+1)] | |
R=[binomial(C,K-k) for k in range(X+1)] | |
CONV=FFT(mod) | |
S=CONV.convolution(CONV.convolution(P,Q),R) | |
if len(S)>=2*K+1: | |
print(S[2*K]) | |
else: | |
print(0) |
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