import sys
readline=sys.stdin.readline

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 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 Primitive_Root(p):
    if p==2:
        return 1
    if p==167772161:
        return 3
    if p==469762049:
        return 3
    if p==754974721:
        return 11
    if p==998244353:
        return 3
    if p==10**9+7:
        return 5
    divisors=[2]
    pp=(p-1)//2
    while pp%2==0:
        pp//=2
    for d in range(3,pp+1,2):
        if d**2>pp:
            break
        if pp%d==0:
            divisors.append(d)
            while pp%d==0:
                pp//=d
    if pp>1:
        divisors.append(pp)
    primitive_root=2
    while True:
        for d in divisors:
            if pow(primitive_root,(p-1)//d,p)==1:
                break
        else:
            return primitive_root
        primitive_root+=1

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 __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 __rtruediv__(self,other):
        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,mod-1>>bit,mod)
                        U=[1]
                        for _ in range(a):
                            U.append(U[-1]*x%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])%mod,(polynomial[s]-polynomial[t]*U[j])%mod
                    x=pow((mod+1)//2,n,mod)
                    for i in range(1<<n):
                        polynomial[i]*=x
                        polynomial[i]%=mod
                else:
                    for bit in range(n,0,-1):
                        a=1<<bit-1
                        x=pow(prim_root_inve,mod-1>>bit,mod)
                        U=[1]
                        for _ in range(a):
                            U.append(U[-1]*x%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])%mod,U[j]*(polynomial[s]-polynomial[t])%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
            if self.mod:
                polynomial=[x*y*y%self.mod for x,y in zip(DFT(self.polynomial[:1<<n+1],n+2),DFT(prev,n+2))]
                quot=DFT(polynomial,n+2,inverse=True)[:1<<n+1]
            else:
                polynomial=[x*y*y for x,y in zip(DFT(self.polynomial[:1<<n+1],n+2),DFT(prev,n+2))]
                quot=DFT(polynomial,n+2,inverse=True)[:1<<n+1]
            for i in range(1<<n):
                quot[i]=2*prev[i]-quot[i]
                if self.mod:
                    quot[i]%=self.mod
            for i in range(1<<n,1<<n+1):
                quot[i]=-quot[i]
                if self.mod:
                    quot[i]%=self.mod
        quot=quot[:self.max_degree+1]
        for i in range(len(quot)):
            quot[i]*=other
            if self.mod:
                quot[i]%=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 Degree(self):
        return len(self.polynomial)-1

def NTT(polynomial0,polynomial1):
    if mod==998244353:
        prim_root=3
        prim_root_inve=332748118
    else:
        prim_root=Primitive_Root(mod)
        prim_root_inve=MOD(mod).Pow(prim_root,-1)
    def DFT(polynomial,n,inverse=False):
        if inverse:
            for bit in range(1,n+1):
                a=1<<bit-1
                x=pow(prim_root,mod-1>>bit,mod)
                U=[1]
                for _ in range(a):
                    U.append(U[-1]*x%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])%mod,(polynomial[s]-polynomial[t]*U[j])%mod
            x=pow((mod+1)//2,n,mod)
            for i in range(1<<n):
                polynomial[i]*=x
                polynomial[i]%=mod
        else:
            for bit in range(n,0,-1):
                a=1<<bit-1
                x=pow(prim_root_inve,mod-1>>bit,mod)
                U=[1]
                for _ in range(a):
                    U.append(U[-1]*x%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])%mod,U[j]*(polynomial[s]-polynomial[t])%mod

    l=len(polynomial0)+len(polynomial1)-1
    n=(len(polynomial0)+len(polynomial1)-2).bit_length()
    polynomial0=polynomial0+[0]*((1<<n)-len(polynomial0))
    polynomial1=polynomial1+[0]*((1<<n)-len(polynomial1))
    DFT(polynomial0,n)
    DFT(polynomial1,n)
    ntt=[x*y%mod for x,y in zip(polynomial0,polynomial1)]
    DFT(ntt,n,inverse=True)
    ntt=ntt[:l]
    return ntt

def Bostan_Mori(poly_nume,poly_deno,N,mod=0,fft=False,ntt=False):
    if type(poly_nume)==Polynomial:
        poly_nume=poly_nume.polynomial
    if type(poly_deno)==Polynomial:
        poly_deno=poly_deno.polynomial
    if ntt:
        convolve=NTT
    elif fft:
        convolve=FFT
    else:
        def convolve(poly_nume,poly_deno):
            conv=[0]*(len(poly_nume)+len(poly_deno)-1)
            for i in range(len(poly_nume)):
                for j in range(len(poly_deno)):
                    conv[i+j]+=poly_nume[i]*poly_deno[j]
            if mod:
                for i in range(len(conv)):
                    conv[i]%=mod
            return conv
    while N:
        poly_deno_=[-x if i%2 else x for i,x in enumerate(poly_deno)]
        if N%2:
            poly_nume=convolve(poly_nume,poly_deno_)[1::2]
        else:
            poly_nume=convolve(poly_nume,poly_deno_)[::2]
        poly_deno=convolve(poly_deno,poly_deno_)[::2]
        if fft and mod:
            for i in range(len(poly_nume)):
                poly_nume[i]%=mod
            for i in range(len(poly_deno)):
                poly_deno[i]%=mod
        N//=2
    return poly_nume[0]

class Matrix:
    def __init__(self,H=0,W=0,matrix=False,eps=0,mod=0,identity=0):
        if identity:
            if H:
                self.H=H
                self.W=H
            else:
                self.H=W
                self.W=W
            self.matrix=[[0]*self.W for i in range(self.H)]
            for i in range(self.H):
                self.matrix[i][i]=identity
        elif matrix:
            self.matrix=matrix
            self.H=len(self.matrix)
            self.W=len(self.matrix[0]) if self.matrix else 0
        else:
            self.H=H
            self.W=W
            self.matrix=[[0]*self.W for i in range(self.H)]
        self.mod=mod
        self.eps=eps

    def __eq__(self,other):
        if type(other)!=Matrix:
            return False
        if self.H!=other.H:
            return False
        if self.mod:
            for i in range(self.H):
                for j in range(self.W):
                    if self.matrix[i][j]%self.mod!=other.matrix[i][j]%self.mod:
                        return False
        else:
            for i in range(self.H):
                for j in range(self.W):
                    if self.eps<abs(self.matrix[i][j]-other.matrix[i][j]):
                        return False
        return True

    def __ne__(self,other):
        if type(other)!=Matrix:
            return True
        if self.H!=other.H:
            return True
        if self.mod:
            for i in range(self.H):
                for j in range(self.W):
                    if self.matrix[i][j]%self.mod!=other.matrix[i][j]%self.mod:
                        return True
        else:
            for i in range(self.H):
                for j in range(self.W):
                    if self.eps<abs(self.matrix[i][j]-other.matrix[i][j]):
                        return True
        return False

    def __add__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            if self.mod:
                summ=Matrix(matrix=[[(self.matrix[i][j]+other.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                summ=Matrix(matrix=[[self.matrix[i][j]+other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            if self.mod:
                summ=Matrix(matrix=[[(self.matrix[i][j]+other)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                summ=Matrix(matrix=[[self.matrix[i][j]+other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return summ

    def __sub__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            if self.mod:
                diff=Matrix(matrix=[[(self.matrix[i][j]-other.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                diff=Matrix(matrix=[[self.matrix[i][j]-other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            if self.mod:
                diff=Matrix(matrix=[[(self.matrix[i][j]-other)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                diff=Matrix(matrix=[[self.matrix[i][j]-other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return diff

    def __mul__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            if self.mod:
                prod=Matrix(matrix=[[(self.matrix[i][j]*other.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                prod=Matrix(matrix=[[self.matrix[i][j]*other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            if self.mod:
                prod=Matrix(matrix=[[(self.matrix[i][j]*other)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                prod=Matrix(matrix=[[self.matrix[i][j]*other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return prod

    def __matmul__(self,other):
        if type(other)==Matrix:
            assert self.W==other.H
            prod=Matrix(H=self.H,W=other.W,eps=self.eps,mod=self.mod)
            for i in range(self.H):
                for j in range(other.W):
                    for k in range(self.W):
                        prod.matrix[i][j]+=self.matrix[i][k]*other.matrix[k][j]
                        if self.mod:
                            prod.matrix[i][j]%=self.mod
        elif type(other)==int:
            assert self.H==self.W
            if other==0:
                prod=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1)
            elif other==1:
                prod=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                prod=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1)
                doub=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
                while other>=2:
                    if other&1:
                        prod@=doub
                    doub@=doub
                    other>>=1
                prod@=doub
        return prod

    def __truediv__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            if self.mod:
                quot=Matrix(matrix=[[(self.matrix[i][j]*MOD(self.mod).Pow(other.matrix[i][j],-1))%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                quot=Matrix(matrix=[[self.matrix[i][j]/other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            if self.mod:
                inve=MOD(self.mod).Pow(other,-1)
                quot=Matrix(matrix=[[(self.matrix[i][j]*inve)%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                quot=Matrix(matrix=[[self.matrix[i][j]/other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return quot

    def __floordiv__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            quot=Matrix(matrix=[[self.matrix[i][j]//other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            quot=Matrix(matrix=[[self.matrix[i][j]//other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return quot

    def __mod__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            rema=Matrix(matrix=[[self.matrix[i][j]%other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            rema=Matrix(matrix=[[self.matrix[i][j]%other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return rema

    def __pow__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            if self.mod:
                powe=Matrix(matrix=[[pow(self.matrix[i][j],other.matrix[i][j],self.mod) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                powe=Matrix(matrix=[[pow(self.matrix[i][j],other.matrix[i][j]) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            if self.mod:
                powe=Matrix(matrix=[[pow(self.matrix[i][j],other,self.mod) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                powe=Matrix(matrix=[[pow(self.matrix[i][j],other) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return powe

    def __lshift__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            lshi=Matrix(matrix=[[self.matrix[i][j]<<other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            lshi=Matrix(matrix=[[self.matrix[i][j]<<other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return lshi

    def __rshift__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            rshi=Matrix(matrix=[[self.matrix[i][j]>>other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            rshi=Matrix(matrix=[[self.matrix[i][j]>>other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return rshi

    def __and__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            conj=Matrix(matrix=[[self.matrix[i][j]&other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            conj=Matrix(matrix=[[self.matrix[i][j]&other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return conj

    def __or__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            disj=Matrix(matrix=[[self.matrix[i][j]|other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            disj=Matrix(matrix=[[self.matrix[i][j]|other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return disj

    def __xor__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            excl=Matrix(matrix=[[self.matrix[i][j]^other.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            excl=Matrix(matrix=[[self.matrix[i][j]^other for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return excl

    def __iadd__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]+=other.matrix[i][j]
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]+=other
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        return self

    def __isub__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]-=other.matrix[i][j]
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]-=other
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        return self

    def __imul__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]*=other.matrix[i][j]
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]*=other
                    if self.mod:
                        self.matrix[i][j]%=self.mod
        return self

    def __imatmul__(self,other):
        if type(other)==Matrix:
            assert self.W==other.H
            prod=Matrix(H=self.H,W=other.W,eps=self.eps,mod=self.mod)
            for i in range(self.H):
                for j in range(other.W):
                    for k in range(self.W):
                        prod.matrix[i][j]+=self.matrix[i][k]*other.matrix[k][j]
                        if self.mod:
                            prod.matrix[i][j]%=self.mod
        elif type(other)==int:
            assert self.H==self.W
            if other==0:
                return Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1)
            elif other==1:
                prod=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
            else:
                prod=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1)
                doub=self
                while other>=2:
                    if other&1:
                        prod@=doub
                    doub@=doub
                    other>>=1
                prod@=doub
        return prod

    def __itruediv__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    if self.mod:
                        self.matrix[i][j]=self.matrix[i][j]*MOD(self.mod).Pow(other.matrix[i][j],-1)%self.mod
                    else:
                        self.matrix[i][j]/=other.matrix[i][j]
        else:
            if self.mod:
                inve=MOD(self.mod).Pow(other,-1)
            for i in range(self.H):
                for j in range(self.W):
                    if self.mod:
                        self.matrix[i][j]=self.matrix[i][j]*inve%self.mod
                    else:
                        self.matrix[i][j]/=other
        return self

    def __ifloordiv__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]//=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]//=other
        return self

    def __imod__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]%=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]%=other
        return self

    def __ipow__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    if self.mod:
                        self.matrix[i][j]=pow(self.matrix[i][j],other.matrix[i][j],self.mod)
                    else:
                        self.matrix[i][j]=pow(self.matrix[i][j],other.matrix[i][j])
        else:
            for i in range(self.H):
                for j in range(self.W):
                    if self.mod:
                        self.matrix[i][j]=pow(self.matrix[i][j],other,self.mod)
                    else:
                        self.matrix[i][j]=pow(self.matrix[i][j],other)
        return self

    def __ilshift__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]<<=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]<<=other
        return self

    def __irshift__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]>>=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]>>=other
        return self

    def __iand__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]&=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]&=other
        return self

    def __ior__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]|=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]|=other
        return self

    def __ixor__(self,other):
        if type(other)==Matrix:
            assert self.H==other.H
            assert self.W==other.W
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]^=other.matrix[i][j]
        else:
            for i in range(self.H):
                for j in range(self.W):
                    self.matrix[i][j]^=other
        return self

    def __neg__(self):
        if self.mod:
            nega=Matrix(matrix=[[(-self.matrix[i][j])%self.mod for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        else:
            nega=Matrix(matrix=[[-self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return nega

    def __pos__(self):
        posi=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return posi

    def __invert__(self):
        inve=Matrix(matrix=[[~self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return inve

    def __abs__(self):
        abso=Matrix(matrix=[[abs(self.matrix[i][j]) for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        return abso

    def __getitem__(self,i):
        if type(i)==int:
            return self.matrix[i]
        elif type(i)==tuple:
            i,j=i
            if type(i)==int:
                i=slice(i,i+1)
            if type(j)==int:
                j=slice(j,j+1)
            return Matrix(matrix=[lst[j] for lst in self.matrix[i]],eps=self.eps,mod=self.mod)

    def __contains__(self,x):
        for i in range(self.H):
            if x in self.matrix[i]:
                return True
        return False

    def __str__(self):
        digit=[max(len(str(self.matrix[i][j])) for i in range(self.H)) for j in range(self.W)]
        return "\n".join([(" [" if i else "[[")+", ".join([str(self.matrix[i][j]).rjust(digit[j]," ") for j in range(self.W)])+"]" for i in range(self.H)])+"]"

    def __bool__(self):
        return True

    def Transpose(self):
        return Matrix(matrix=[[self.matrix[i][j] for i in range(self.H)] for j in range(self.W)])

    def Trace(self):
        assert self.H==self.W
        trace=sum(self.matrix[i][i] for i in range(self.H))
        if self.mod:
            trace%=self.mod
        return trace

    def Elem_Raw_Operate_1(self,i0,i1):
        self.matrix[i0],self.matrix[i1]=self.matrix[i1],self.matrix[i0]

    def Elem_Raw_Operate_2(self,i,c):
        if self.mod:
            self.matrix[i]=[self.matrix[i][j]*c%self.mod for j in range(self.W)]
        else:
            self.matrix[i]=[self.matrix[i][j]*c for j in range(self.W)]

    def Elem_Raw_Operate_3(self,i0,i1,c):
        if self.mod:
            self.matrix[i0]=[(self.matrix[i0][j]+c*self.matrix[i1][j])%self.mod for j in range(self.W)]
        else:
            self.matrix[i0]=[self.matrix[i0][j]+c*self.matrix[i1][j] for j in range(self.W)]

    def Elimination(self,determinant=False,inverse_matrix=False,linear_equation=False,rank=False,upper_triangular=False):
        h=0
        ut=Matrix(matrix=[[self.matrix[i][j] for j in range(self.W)] for i in range(self.H)],eps=self.eps,mod=self.mod)
        if determinant or inverse_matrix:
            assert self.H==self.W
            det=1
        if inverse_matrix:
            assert self.H==self.W
            im=Matrix(H=self.H,eps=self.eps,mod=self.mod,identity=1)
        if linear_equation:
            assert self.H==linear_equation.H
            le=Matrix(matrix=[[linear_equation.matrix[i][j] for j in range(linear_equation.W)] for i in range(linear_equation.H)],eps=self.eps,mod=self.mod)
        for j in range(ut.W):
            for i in range(h,ut.H):
                if abs(ut.matrix[i][j])>ut.eps:
                    if determinant or inverse_matrix:
                        det*=ut.matrix[i][j]
                        if self.mod:
                            det%=self.mod
                    if self.mod:
                        inve=MOD(self.mod).Pow(ut.matrix[i][j],-1)
                    else:
                        inve=1/ut.matrix[i][j]

                    ut.Elem_Raw_Operate_1(i,h)
                    if determinant and i!=h and self.mod:
                        det=(-det)%self.mod
                    if inverse_matrix:
                        im.Elem_Raw_Operate_1(i,h)
                    if linear_equation:
                        le.Elem_Raw_Operate_1(i,h)

                    ut.Elem_Raw_Operate_2(h,inve)
                    if inverse_matrix:
                        im.Elem_Raw_Operate_2(h,inve)
                    if linear_equation:
                        le.Elem_Raw_Operate_2(h,inve)

                    for ii in range(ut.H):
                        if ii==h:
                            continue
                        x=-ut.matrix[ii][j]
                        ut.Elem_Raw_Operate_3(ii,h,x)
                        if inverse_matrix:
                            im.Elem_Raw_Operate_3(ii,h,x)
                        if linear_equation:
                            le.Elem_Raw_Operate_3(ii,h,x)
                    h+=1
                    break
            else:
                det=0
        if any(le[i][0] for i in range(h,self.H)):
            le=None
        tpl=()
        if determinant:
            tpl+=(det,)
        if inverse_matrix:
            if det==0:
                im=None
            tpl+=(im,)
        if linear_equation:
            tpl+=(le,)
        if rank:
            tpl+=(h,)
        if upper_triangular:
            tpl+=(ut,)
        if len(tpl)==1:
            tpl=tpl[0]
        return tpl

mod=998244353
N,K=map(int,readline().split())
M=Matrix(2*K**2,2*K**2,mod=mod)
for i in range(K):
    for j in range(K):
        for k in range(K):
            if len({i,j,k})==3 and j in (min(i,j,k),max(i,j,k)):
                M[i*K+j][j*K+k]+=1
                M[K**2+i*K+j][K**2+j*K+k]+=1
                M[i*K+j][K**2+j*K+k]+=k
A=Matrix(1,2*K**2,mod=mod)
for i in range(K**2):
    A[0][i]=1
    A[0][i+K**2]+=i//K+i%K
A@=M@(N-2)
print(sum(A[0][:K**2])%mod,sum(A[0][K**2:])%mod)