結果
問題 | No.2770 Coupon Optimization |
ユーザー |
![]() |
提出日時 | 2024-05-31 22:08:39 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 1,280 ms / 3,000 ms |
コード長 | 7,199 bytes |
コンパイル時間 | 427 ms |
コンパイル使用メモリ | 82,484 KB |
実行使用メモリ | 149,120 KB |
最終ジャッジ日時 | 2024-12-20 23:40:28 |
合計ジャッジ時間 | 17,895 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge4 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 2 |
other | AC * 16 |
ソースコード
class FFT():def primitive_root_constexpr(self,m):if m==2:return 1if m==167772161:return 3if m==469762049:return 3if m==754974721:return 11if m==998244353:return 3divs=[0]*20divs[0]=2cnt=1x=(m-1)//2while(x%2==0):x//=2i=3while(i*i<=x):if (x%i==0):divs[cnt]=icnt+=1while(x%i==0):x//=ii+=2if x>1:divs[cnt]=xcnt+=1g=2while(1):ok=Truefor i in range(cnt):if pow(g,(m-1)//divs[i],m)==1:ok=Falsebreakif ok:return gg+=1def bsf(self,x):res=0while(x%2==0):res+=1x//=2return resrank2=0root=[]iroot=[]rate2=[]irate2=[]rate3=[]irate3=[]def __init__(self,MOD):self.mod=MODself.g=self.primitive_root_constexpr(self.mod)self.rank2=self.bsf(self.mod-1)self.root=[0 for i in range(self.rank2+1)]self.iroot=[0 for i in range(self.rank2+1)]self.rate2=[0 for i in range(self.rank2)]self.irate2=[0 for i in range(self.rank2)]self.rate3=[0 for i in range(self.rank2-1)]self.irate3=[0 for i in range(self.rank2-1)]self.root[self.rank2]=pow(self.g,(self.mod-1)>>self.rank2,self.mod)self.iroot[self.rank2]=pow(self.root[self.rank2],self.mod-2,self.mod)for i in range(self.rank2-1,-1,-1):self.root[i]=(self.root[i+1]**2)%self.modself.iroot[i]=(self.iroot[i+1]**2)%self.modprod=1;iprod=1for i in range(self.rank2-1):self.rate2[i]=(self.root[i+2]*prod)%self.modself.irate2[i]=(self.iroot[i+2]*iprod)%self.modprod=(prod*self.iroot[i+2])%self.modiprod=(iprod*self.root[i+2])%self.modprod=1;iprod=1for i in range(self.rank2-2):self.rate3[i]=(self.root[i+3]*prod)%self.modself.irate3[i]=(self.iroot[i+3]*iprod)%self.modprod=(prod*self.iroot[i+3])%self.modiprod=(iprod*self.root[i+3])%self.moddef butterfly(self,a):n=len(a)h=(n-1).bit_length()LEN=0while(LEN<h):if (h-LEN==1):p=1<<(h-LEN-1)rot=1for s in range(1<<LEN):offset=s<<(h-LEN)for i in range(p):l=a[i+offset]r=a[i+offset+p]*rota[i+offset]=(l+r)%self.moda[i+offset+p]=(l-r)%self.modrot*=self.rate2[(~s & -~s).bit_length()-1]rot%=self.modLEN+=1else:p=1<<(h-LEN-2)rot=1imag=self.root[2]for s in range(1<<LEN):rot2=(rot*rot)%self.modrot3=(rot2*rot)%self.modoffset=s<<(h-LEN)for i in range(p):a0=a[i+offset]a1=a[i+offset+p]*rota2=a[i+offset+2*p]*rot2a3=a[i+offset+3*p]*rot3a1na3imag=(a1-a3)%self.mod*imaga[i+offset]=(a0+a2+a1+a3)%self.moda[i+offset+p]=(a0+a2-a1-a3)%self.moda[i+offset+2*p]=(a0-a2+a1na3imag)%self.moda[i+offset+3*p]=(a0-a2-a1na3imag)%self.modrot*=self.rate3[(~s & -~s).bit_length()-1]rot%=self.modLEN+=2def butterfly_inv(self,a):n=len(a)h=(n-1).bit_length()LEN=hwhile(LEN):if (LEN==1):p=1<<(h-LEN)irot=1for s in range(1<<(LEN-1)):offset=s<<(h-LEN+1)for i in range(p):l=a[i+offset]r=a[i+offset+p]a[i+offset]=(l+r)%self.moda[i+offset+p]=(l-r)*irot%self.modirot*=self.irate2[(~s & -~s).bit_length()-1]irot%=self.modLEN-=1else:p=1<<(h-LEN)irot=1iimag=self.iroot[2]for s in range(1<<(LEN-2)):irot2=(irot*irot)%self.modirot3=(irot*irot2)%self.modoffset=s<<(h-LEN+2)for i in range(p):a0=a[i+offset]a1=a[i+offset+p]a2=a[i+offset+2*p]a3=a[i+offset+3*p]a2na3iimag=(a2-a3)*iimag%self.moda[i+offset]=(a0+a1+a2+a3)%self.moda[i+offset+p]=(a0-a1+a2na3iimag)*irot%self.moda[i+offset+2*p]=(a0+a1-a2-a3)*irot2%self.moda[i+offset+3*p]=(a0-a1-a2na3iimag)*irot3%self.modirot*=self.irate3[(~s & -~s).bit_length()-1]irot%=self.modLEN-=2def convolution(self,a,b):n=len(a);m=len(b)if not(a) or not(b):return []if min(n,m)<=40: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.modreturn resz=1<<((n+m-2).bit_length())a=a+[0]*(z-n)b=b+[0]*(z-m)self.butterfly(a)self.butterfly(b)c=[(a[i]*b[i])%self.mod for i in range(z)]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.modreturn c[:n+m-1]def inv_gcd(a,b):a=a%bif a==0:return (b,0)s=b;t=am0=0;m1=1while(t):u=s//ts-=t*um0-=m1*us,t=t,sm0,m1=m1,m0if m0<0:m0+=b//sreturn (s,m0)def crt(r,m):assert len(r)==len(m)n=len(r)r0=0;m0=1for i in range(n):assert 1<=m[i]r1=r[i]%m[i]m1=m[i]if m0<m1:r0,r1=r1,r0m0,m1=m1,m0if (m0%m1==0):if (r0%m1!=r1):return (0,0)continueg,im=inv_gcd(m0,m1)u1=m1//gif ((r1-r0)%g):return (0,0)x=(r1-r0)//g % u1*im%u1r0+=x*m0m0*=u1if r0<0:r0+=m0return (r0,m0)mod1 = 998244353; mod2 = 1012924417n,m = map(int,input().split())a = sorted(v//100 for v in map(int,input().split()))b = sorted(100-v for v in map(int,input().split()))+[100]*max(n-m,0)c1 = FFT(mod1).convolution(a,b); c2 = FFT(mod2).convolution(a,b)for i in range(n): print(crt([c1[i],c2[i]],[mod1,mod2])[0])