結果

問題 No.868 ハイパー部分和問題
ユーザー vwxyz
提出日時 2024-04-15 11:08:44
言語 PyPy3
(7.3.15)
結果
WA  
実行時間 -
コード長 25,054 bytes
コンパイル時間 250 ms
コンパイル使用メモリ 82,304 KB
実行使用メモリ 84,224 KB
最終ジャッジ日時 2024-10-05 06:10:05
合計ジャッジ時間 10,736 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge4
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 -- * 2
other AC * 13 WA * 1 TLE * 1 -- * 23
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

import random
class Polynomial:
    def __init__(self,polynomial,max_degree=-1,eps=0,mod=0):
        self.max_degree=max_degree
        if self.max_degree!=-1 and len(polynomial)>self.max_degree+1:
            self.polynomial=polynomial[:self.max_degree+1]
        else:
            self.polynomial=polynomial
        self.mod=mod
        self.eps=eps
    def __eq__(self,other):
        if type(other)!=Polynomial:
            return False
        if len(self.polynomial)!=len(other.polynomial):
            return False
        for i in range(len(self.polynomial)):
            if self.eps<abs(self.polynomial[i]-other.polynomial[i]):
                return False
        return True
    def __ne__(self,other):
        if type(other)!=Polynomial:
            return True
        if len(self.polynomial)!=len(other.polynomial):
            return True
        for i in range(len(self.polynomial)):
            if self.eps<abs(self.polynomial[i]-other.polynomial[i]):
                return True
        return False
    def __add__(self,other):
        if type(other)==Polynomial:
            summ=[0]*max(len(self.polynomial),len(other.polynomial))
            for i in range(len(self.polynomial)):
                summ[i]+=self.polynomial[i]
            for i in range(len(other.polynomial)):
                summ[i]+=other.polynomial[i]
            if self.mod:
                for i in range(len(summ)):
                    summ[i]%=self.mod
        else:
            summ=[x for x in self.polynomial] if self.polynomial else [0]
            summ[0]+=other
            if self.mod:
                summ[0]%=self.mod
        while summ and abs(summ[-1])<=self.eps:
            summ.pop()
        summ=Polynomial(summ,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return summ
    def __sub__(self,other):
        if type(other)==Polynomial:
            diff=[0]*max(len(self.polynomial),len(other.polynomial))
            for i in range(len(self.polynomial)):
                diff[i]+=self.polynomial[i]
            for i in range(len(other.polynomial)):
                diff[i]-=other.polynomial[i]
            if self.mod:
                for i in range(len(diff)):
                    diff[i]%=self.mod
        else:
            diff=[x for x in self.polynomial] if self.polynomial else [0]
            diff[0]-=other
            if self.mod:
                diff[0]%=self.mod
        while diff and abs(diff[-1])<=self.eps:
            diff.pop()
        diff=Polynomial(diff,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return diff
    def __mul__(self,other):
        if type(other)==Polynomial:
            if self.max_degree==-1:
                prod=[0]*(len(self.polynomial)+len(other.polynomial)-1)
                for i in range(len(self.polynomial)):
                    for j in range(len(other.polynomial)):
                        prod[i+j]+=self.polynomial[i]*other.polynomial[j]
            else:
                prod=[0]*min(len(self.polynomial)+len(other.polynomial)-1,self.max_degree+1)
                for i in range(len(self.polynomial)):
                    for j in range(min(len(other.polynomial),self.max_degree+1-i)):
                        prod[i+j]+=self.polynomial[i]*other.polynomial[j]
            if self.mod:
                for i in range(len(prod)):
                    prod[i]%=self.mod
        else:
            if self.mod:
                prod=[x*other%self.mod for x in self.polynomial]
            else:
                prod=[x*other for x in self.polynomial]
        while prod and abs(prod[-1])<=self.eps:
            prod.pop()
        prod=Polynomial(prod,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return prod
    def __matmul__(self,other):
        assert type(other)==Polynomial
        if self.mod:
            prod=NTT(self.polynomial,other.polynomial)
        else:
            prod=FFT(self.polynomial,other.polynomial)
        if self.max_degree!=-1 and len(prod)>self.max_degree+1:
            prod=prod[:self.max_degree+1]
            while prod and abs(prod[-1])<=self.eps:
                prod.pop()
        prod=Polynomial(prod,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return prod
    def __pow__(self,other):
        if other==0:
            prod=Polynomial([1],max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        elif other==1:
            prod=Polynomial([x for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        else:
            prod=[1]
            doub=self.polynomial
            if self.mod:
                convolve=NTT
                convolve_Pow=NTT_Pow
            else:
                convolve=FFT
                convolve_Pow=FFT_Pow
            while other>=2:
                if other&1:
                    prod=convolve(prod,doub)
                    if self.max_degree!=-1:
                        prod=prod[:self.max_degree+1]
                doub=convolve_Pow(doub,2)
                if self.max_degree!=-1:
                    doub=doub[:self.max_degree+1]
                other>>=1
            prod=convolve(prod,doub)
            if self.max_degree!=-1:
                prod=prod[:self.max_degree+1]
            prod=Polynomial(prod,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return prod
    def __truediv__(self,other):
        if type(other)==Polynomial:
            assert other.polynomial
            for n in range(len(other.polynomial)):
                if self.eps<abs(other.polynomial[n]):
                    break
            assert len(self.polynomial)>n
            for i in range(n):
                assert abs(self.polynomial[i])<=self.eps
            self_polynomial=self.polynomial[n:]
            other_polynomial=other.polynomial[n:]
            if self.mod:
                inve=MOD(self.mod).Pow(other_polynomial[0],-1)
            else:
                inve=1/other_polynomial[0]
            quot=[]
            for i in range(len(self_polynomial)-len(other_polynomial)+1):
                if self.mod:
                    quot.append(self_polynomial[i]*inve%self.mod)
                else:
                    quot.append(self_polynomial[i]*inve)
                for j in range(len(other_polynomial)):
                    self_polynomial[i+j]-=other_polynomial[j]*quot[-1]
                    if self.mod:
                        self_polynomial[i+j]%=self.mod
            for i in range(max(0,len(self_polynomial)-len(other_polynomial)+1),len(self_polynomial)):
                if self.eps<abs(self_polynomial[i]):
                    assert self.max_degree!=-1
                    self_polynomial=self_polynomial[-len(other_polynomial)+1:]+[0]*(len(other_polynomial)-1-len(self_polynomial))
                    while len(quot)<=self.max_degree:
                        self_polynomial.append(0)
                        if self.mod:
                            quot.append(self_polynomial[0]*inve%self.mod)
                            self_polynomial=[(self_polynomial[i]-other_polynomial[i]*quot[-1])%self.mod for i in range(1,len(self_polynomial))]
                        else:
                            quot.append(self_polynomial[0]*inve)
                            self_polynomial=[(self_polynomial[i]-other_polynomial[i]*quot[-1]) for i in range(1,len(self_polynomial))]
                    break
            quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        else:
            assert self.eps<abs(other)
            if self.mod:
                inve=MOD(self.mod).Pow(other,-1)
                quot=Polynomial([x*inve%self.mod for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod)
            else:
                quot=Polynomial([x/other for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return quot
    def __floordiv__(self,other):
        assert type(other)==Polynomial
        quot=[0]*(len(self.polynomial)-len(other.polynomial)+1)
        rema=[x for x in self.polynomial]
        if self.mod:
            inve=MOD(self.mod).Pow(other.polynomial[-1],-1)
            for i in range(len(self.polynomial)-len(other.polynomial),-1,-1):
                quot[i]=rema[i+len(other.polynomial)-1]*inve%self.mod
                for j in range(len(other.polynomial)):
                    rema[i+j]-=quot[i]*other.polynomial[j]
                    rema[i+j]%=self.mod
        else:
            inve=1/other.polynomial[-1]
            for i in range(len(self.polynomial)-len(other.polynomial),-1,-1):
                quot[i]=rema[i+len(other.polynomial)-1]*inve
                for j in range(len(other.polynomial)):
                    rema[i+j]-=quot[i]*other.polynomial[j]
        quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return quot
    def __mod__(self,other):
        assert type(other)==Polynomial
        quot=[0]*(len(self.polynomial)-len(other.polynomial)+1)
        rema=[x for x in self.polynomial]
        if self.mod:
            inve=MOD(self.mod).Pow(other.polynomial[-1],-1)
            for i in range(len(self.polynomial)-len(other.polynomial),-1,-1):
                quot[i]=rema[i+len(other.polynomial)-1]*inve%self.mod
                for j in range(len(other.polynomial)):
                    rema[i+j]-=quot[i]*other.polynomial[j]
                    rema[i+j]%=self.mod
        else:
            inve=1/other.polynomial[-1]
            for i in range(len(self.polynomial)-len(other.polynomial),-1,-1):
                quot[i]=rema[i+len(other.polynomial)-1]*inve
                for j in range(len(other.polynomial)):
                    rema[i+j]-=quot[i]*other.polynomial[j]
        while rema and abs(rema[-1])<=self.eps:
            rema.pop()
        rema=Polynomial(rema,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return rema
    def __divmod__(self,other):
        assert type(other)==Polynomial
        quot=[0]*(len(self.polynomial)-len(other.polynomial)+1)
        rema=[x for x in self.polynomial]
        if self.mod:
            inve=MOD(self.mod).Pow(other.polynomial[-1],-1)
            for i in range(len(self.polynomial)-len(other.polynomial),-1,-1):
                quot[i]=rema[i+len(other.polynomial)-1]*inve%self.mod
                for j in range(len(other.polynomial)):
                    rema[i+j]-=quot[i]*other.polynomial[j]
                    rema[i+j]%=self.mod
        else:
            inve=1/other.polynomial[-1]
            for i in range(len(self.polynomial)-len(other.polynomial),-1,-1):
                quot[i]=rema[i+len(other.polynomial)-1]*inve
                for j in range(len(other.polynomial)):
                    rema[i+j]-=quot[i]*other.polynomial[j]
        while rema and abs(rema[-1])<=self.eps:
            rema.pop()
        quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        rema=Polynomial(rema,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return quot,rema
    def __neg__(self):
        if self.mod:
            nega=Polynomial([(-x)%self.mod for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        else:
            nega=Polynomial([-x for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return nega
    def __pos__(self):
        posi=Polynomial([x for x in self.polynomial],max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return posi
    def __bool__(self):
        return self.polynomial
    def __getitem__(self,n):
        if type(n)==int:
            if n<=len(self.polynomial)-1:
                return self.polynomial[n]
            else:
                return 0
        else:
            return Polynomial(polynomial=self.polynomial[n],max_degree=self.max_degree,eps=self.eps,mod=self.mod)
    
    def __setitem__(self,n,a):
        if self.mod:
            a%=self.mod
        if self.max_degree==-1 or n<=self.max_degree:
            if n<=len(self.polynomial)-1:
                self.polynomial[n]=a
            elif self.eps<abs(a):
                self.polynomial+=[0]*(n-len(self.polynomial))+[a]
    def __iter__(self):
        for x in self.polynomial:
            yield x
    def __call__(self,x):
        retu=0
        pow_x=1
        for i in range(len(self.polynomial)):
            retu+=pow_x*self.polynomial[i]
            pow_x*=x
            if self.mod:
                retu%=self.mod
                pow_x%=self.mod
        return retu
    def __str__(self):
        return "["+", ".join(map(str,self.polynomial))+"]"
    def __len__(self):
        return len(self.polynomial)
    def Differentiate(self):
        if self.mod:
            differential=[x*i%self.mod for i,x in enumerate(self.polynomial[1:],1)]
        else:
            differential=[x*i for i,x in enumerate(self.polynomial[1:],1)]
        return Polynomial(differential,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
    def Integrate(self):
        if self.mod:
            MD=MOD(self.mod)
            MD.Build_Inverse(len(self.polynomial))
            integral=[0]+[x*MD.Inverse(i+1)%self.mod for i,x in enumerate(self.polynomial)]
        else:
            integral=[0]+[x/(i+1) for i,x in enumerate(self.polynomial)]
        while integral and abs(integral[-1])<=self.eps:
            integral.pop()
        return Polynomial(integral,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
    def Inverse(self):
        assert self.polynomial and self.eps<self.polynomial[0]
        assert self.max_degree!=-1
        if self.mod:
            quot=[MOD(self.mod).Pow(self.polynomial[0],-1)]
            if self.mod==998244353:
                prim_root=3
                prim_root_inve=332748118
            else:
                prim_root=Primitive_Root(self.mod)
                prim_root_inve=MOD(self.mod).Pow(prim_root,-1)
            def DFT(polynomial,n,inverse=False):
                polynomial=polynomial+[0]*((1<<n)-len(polynomial))
                if inverse:
                    for bit in range(1,n+1):
                        a=1<<bit-1
                        x=pow(prim_root,self.mod-1>>bit,self.mod)
                        U=[1]
                        for _ in range(a):
                            U.append(U[-1]*x%self.mod)
                        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]*U[j])%self.mod,(polynomial[s]-polynomial[t]*U[j])%self.mod
                    x=pow((self.mod+1)//2,n,self.mod)
                    for i in range(1<<n):
                        polynomial[i]*=x
                        polynomial[i]%=self.mod
                else:
                    for bit in range(n,0,-1):
                        a=1<<bit-1
                        x=pow(prim_root_inve,self.mod-1>>bit,self.mod)
                        U=[1]
                        for _ in range(a):
                            U.append(U[-1]*x%self.mod)
                        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])%self.mod,U[j]*(polynomial[s]-polynomial[t])%self.mod
                return polynomial
        else:
            quot=[1/self.polynomial[0]]
            def DFT(polynomial,n,inverse=False):
                N=len(polynomial)
                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)]
                polynomial=polynomial+[0]*((1<<n)-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]
                    for i in range(1<<n):
                        polynomial[i]=round((polynomial[i]/(1<<n)).real)
                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])
                return polynomial
        for n in range(self.max_degree.bit_length()):
            prev=quot
            DFT_prev=DFT(prev,n+1)
            if self.mod:
                quot=[x*y%self.mod for x,y in zip(DFT_prev,DFT(self.polynomial[:1<<n+1],n+1))]
            else:
                quot=[x*y for x,y in zip(DFT_prev,DFT(self.polynomial[:1<<n+1],n+1))]
            quot=DFT([0]*(1<<n)+DFT(quot,n+1,inverse=True)[1<<n:],n+1)
            if self.mod:
                quot=[(-x*y)%self.mod for x,y in zip(DFT_prev,quot)]
            else:
                quot=[-x*y for x,y in zip(DFT_prev,quot)]
            quot=prev+DFT(quot,n+1,inverse=True)[1<<n:]
        quot=quot[:self.max_degree+1]
        quot=Polynomial(quot,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return quot
    def Log(self):
        assert self.max_degree!=-1
        assert self.polynomial and abs(self.polynomial[0]-1)<=self.eps
        log=self.inverse()
        if self.mod:
            log=Polynomial(NTT(self.differentiate().polynomial,log.polynomial),max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        else:
            log=Polynomial(FFT(self.differentiate().polynomial,log.polynomial),max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        log=log.integrate()
        return log
    def Newton(self,n0,f,differentiated_f=None):
        newton=[n0]
        while len(newton)<self.max_degree+1:
            prev=newton
            if differentiated_f==None:
                newton=f(prev,self.polynomial)
            else:
                newton=f(prev)
                for i in range(min(len(self.polynomial),len(newton))):
                    newton[i]-=self.polynomial[i]
                    newton[i]%=self.mod
                if self.mod:
                    newton=NTT(newton,Polynomial(differentiated_f(prev),max_degree=len(newton)-1,eps=self.eps,mod=self.mod).inverse().polynomial)[
                        :len(newton)]
                else:
                    newton=FFT(newton,Polynomial(differentiated_f(prev),max_degree=len(newton)-1,eps=self.eps,mod=self.mod).inverse().polynomial)[
                        :len(newton)]
            for i in range(len(newton)):
                newton[i]=-newton[i]
                newton[i]%=self.mod
            for i in range(len(prev)):
                newton[i]+=prev[i]
                newton[i]%=self.mod
        newton=newton[:self.max_degree+1]
        while newton and newton[-1]<=self.eps:
            newton.pop()
        return Polynomial(newton,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
    def Sqrt(self):
        if self.polynomial:
            for cnt0 in range(len(self.polynomial)):
                if self.polynomial[cnt0]:
                    break
            if cnt0%2:
                sqrt=None
            else:
                if self.mod:
                    n0=Tonelli_Shanks(self.polynomial[cnt0],self.mod)
                else:
                    if self.polynomial[cnt0]>=self.eps:
                        n0=self.polynomial[cnt0]**.5
                if n0==None:
                    sqrt=None
                else:
                    def f(prev):
                        if self.mod:
                            return NTT_Pow(prev,2)+[0]
                        else:
                            return FFT_Pow(prev,2)+[0]
                    def differentiated_f(prev):
                        retu=[0]*(2*len(prev)-1)
                        for i in range(len(prev)):
                            retu[i]+=2*prev[i]
                            if self.mod:
                                retu[i]%self.mod
                        return retu
                    sqrt=[0]*(cnt0//2)+Polynomial(self.polynomial[cnt0:],max_degree=self.max_degree-cnt0//2,mod=self.mod).Newton(n0,f
                        ,differentiated_f).polynomial
                    sqrt=Polynomial(sqrt,max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        else:
            sqrt=Polynomial([],max_degree=self.max_degree,eps=self.eps,mod=self.mod)
        return sqrt
    def Exp(self):
        assert not self.polynomial or abs(self.polynomial[0])<=self.eps
        def f(prev,poly):
            newton=Polynomial(prev,max_degree=2*len(prev)-1,eps=self.eps,mod=self.mod).log().polynomial
            newton+=[0]*(2*len(prev)-len(newton))
            for i in range(min(len(poly),len(newton))):
                newton[i]-=poly[i]
            if self.mod:
                for i in range(len(newton)):
                    newton[i]%=self.mod
            if self.mod:
                return NTT(prev,newton)[:2*len(prev)]
            else:
                return FFT(prev,newton)[:2*len(prev)]
        return Polynomial(self.polynomial,max_degree=self.max_degree,mod=self.mod).Newton(1,f)
    def Degree(self):
        return len(self.polynomial)-1
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
N,K=map(int,input().split())
A=list(map(int,input().split()))
mod=998244353
rand=[random.randint(1<<20,1<<250) for i in range(N)]
P=Polynomial(polynomial=[1],max_degree=K,mod=mod)
for i,a in enumerate(A):
    poly=[0]*(a+1)
    poly[0]=1
    poly[a]=1
    P*=Polynomial(polynomial=poly,max_degree=K,mod=mod)
Q=int(input())
for q in range(Q):
    x,v=map(int,input().split())
    x-=1
    poly=[0]*(A[x]+1)
    poly[0]=1
    poly[A[x]]=1
    P/=Polynomial(polynomial=poly,max_degree=K,mod=mod)
    A[x]=v
    poly=[0]*(A[x]+1)
    poly[0]=1
    poly[A[x]]=1
    P*=Polynomial(polynomial=poly,max_degree=K,mod=mod)
    if P[K]:
        ans=1
    else:
        ans=0
    print(ans)
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0