################################# def mod_pow(a,b,mod): # a^{b} b = int(b) x = 1 for times in range(0,b): x = x * a % mod return x def getg(p): # p-1 の素因数を求める n=p-1 prime_factor_list=[] N=n for q in range(2,n+1): if q**2>n:break if N%q==0: prime_factor_list.append(q) while N%q==0:N//=q k = len(prime_factor_list) # ここからが上のアルゴリズムのStep 3にあたる a = 2 i = 0 while (i != k): if (mod_pow(a, (p - 1) // prime_factor_list[i], p) == 1): a += 1 i = 0 else: i += 1 return a # a がZ/pZの最小原始根 def mulconv(A,B,p,conv): #res[0]だけは998244353で割ってない! A1=[0]*p B1=[0]*p g=getg(p) for i in range(len(A)): A1[i%p]+=A[i] for i in range(len(B)): B1[i%p]+=B[i] A2=[0]*(p-1) B2=[0]*(p-1) for x in range(p-1): A2[x]+=A1[pow(g,x,p)] B2[x]+=B1[pow(g,x,p)] res2=conv(A2,B2) res=[0]*p for x in range(len(res2)): res[pow(g,x,p)]+=res2[x] res[0]=A1[0]*sum(B1)+B1[0]*sum(A1)-A1[0]*B1[0] return res ################################ 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