import math
from functools import lru_cache
#mod = 998244353
imag = 911660635
iimag = 86583718
rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601,
              842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)
irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960,
               354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)
rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,
              183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)
irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500,
               771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)

def butterfly(a):
    n = len(a)
    h = (n - 1).bit_length()
    len_ = 0
    while len_ < h:
        if h - len_ == 1:
            p = 1 << (h - len_ - 1)
            rot = 1
            for s in range(1 << len_):
                offset = s << (h - len_)
                for i in range(p):
                    l = a[i + offset]
                    r = a[i + offset + p] * rot % mod
                    a[i + offset] = (l + r) % mod
                    a[i + offset + p] = (l - r) % mod
                if s + 1 != 1 << len_:
                    rot *= rate2[(~s & -~s).bit_length() - 1]
                    rot %= mod
            len_ += 1
        else:
            p = 1 << (h - len_ - 2)
            rot = 1
            for s in range(1 << len_):
                rot2 = rot * rot % mod
                rot3 = rot2 * rot % mod
                offset = s << (h - len_)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p] * rot
                    a2 = a[i + offset + p * 2] * rot2
                    a3 = a[i + offset + p * 3] * rot3
                    a1na3imag = (a1 - a3) % mod * imag
                    a[i + offset] = (a0 + a2 + a1 + a3) % mod
                    a[i + offset + p] = (a0 + a2 - a1 - a3) % mod
                    a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % mod
                    a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % mod
                if s + 1 != 1 << len_:
                    rot *= rate3[(~s & -~s).bit_length() - 1]
                    rot %= mod
            len_ += 2

def butterfly_inv(a):
    n = len(a)
    h = (n - 1).bit_length()
    len_ = h
    while len_:
        if len_ == 1:
            p = 1 << (h - len_)
            irot = 1
            for 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) % mod
                    a[i + offset + p] = (l - r) * irot % mod
                if s + 1 != (1 << (len_ - 1)):
                    irot *= irate2[(~s & -~s).bit_length() - 1]
                    irot %= mod
            len_ -= 1
        else:
            p = 1 << (h - len_)
            irot = 1
            for s in range(1 << (len_ - 2)):
                irot2 = irot * irot % mod
                irot3 = irot2 * irot % mod
                offset = s << (h - len_ + 2)
                for i in range(p):
                    a0 = a[i + offset]
                    a1 = a[i + offset + p]
                    a2 = a[i + offset + p * 2]
                    a3 = a[i + offset + p * 3]
                    a2na3iimag = (a2 - a3) * iimag % mod
                    a[i + offset] = (a0 + a1 + a2 + a3) % mod
                    a[i + offset + p] = (a0 - a1 + a2na3iimag) * irot % mod
                    a[i + offset + p * 2] = (a0 + a1 - a2 - a3) * irot2 % mod
                    a[i + offset + p * 3] = (a0 - a1 - a2na3iimag) * irot3 % mod
                if s + 1 != (1 << (len_ - 2)):
                    irot *= irate3[(~s & -~s).bit_length() - 1]
                    irot %= mod
            len_ -= 2

def convolution_naive(a, b):
    n = len(a)
    m = len(b)
    ans = [0] * (n + m - 1)
    if n < m:
        for j in range(m):
            for i in range(n):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % mod
    else:
        for i in range(n):
            for j in range(m):
                ans[i + j] = (ans[i + j] + a[i] * b[j]) % mod
    return ans

def convolution_ntt(a, b):
    a = a.copy()
    b = b.copy()
    n = len(a)
    m = len(b)
    z = 1 << (n + m - 2).bit_length()
    a += [0] * (z - n)
    butterfly(a)
    b += [0] * (z - m)
    butterfly(b)
    for i in range(z):
        a[i] = a[i] * b[i] % mod
    butterfly_inv(a)
    a = a[:n + m - 1]
    iz = pow(z, mod - 2, mod)
    for i in range(n + m - 1):
        a[i] = a[i] * iz % mod
    return a

def convolution_square(a):
    a = a.copy()
    n = len(a)
    z = 1 << (2 * n - 2).bit_length()
    a += [0] * (z - n)
    butterfly(a)
    for i in range(z):
        a[i] = a[i] * a[i] % mod
    butterfly_inv(a)
    a = a[:2 * n - 1]
    iz = pow(z, mod - 2, mod)
    for i in range(2 * n - 1):
        a[i] = a[i] * iz % mod
    return a

def convolution(a, b):
    """It calculates (+, x) convolution in mod 998244353. 
    Given two arrays a[0], a[1], ..., a[n - 1] and b[0], b[1], ..., b[m - 1], 
    it calculates the array c of length n + m - 1, defined by

    >   c[i] = sum(a[j] * b[i - j] for j in range(i + 1)) % 998244353.

    It returns an empty list if at least one of a and b are empty.

    Complexity
    ----------

    >   O(n log n), where n = len(a) + len(b).
    """
    n = len(a)
    m = len(b)
    if n == 0 or m == 0:
        return []
    if min(n, m) <= 60:
        return convolution_naive(a, b)
    if a is b:
        return convolution_square(a)
    return convolution_ntt(a, b)

def integrate(a):
    a=a.copy()
    n = len(a)
    assert n > 0
    a.pop()
    a.insert(0, 0)
    inv = [1, 1]
    for i in range(2, n):
        inv.append(-inv[mod%i] * (mod//i) % mod)
        a[i] = a[i] * inv[i] % mod
    return a

def differentiate(a):
    n = len(a)
    assert n > 0
    for i in range(2, n):
        a[i] = a[i] * i % mod
    a.pop(0)
    a.append(0)
    return a

def inverse(a):
    n = len(a)
    assert n > 0 and a[0] != 0
    res = [pow(a[0], mod - 2, mod)]
    m = 1
    while m < n:
        f = a[:min(n,2*m)] + [0]*(2*m-min(n,2*m))
        g = res + [0]*m
        butterfly(f)
        butterfly(g)
        for i in range(2*m):
            f[i] = f[i] * g[i] % mod
        butterfly_inv(f)
        f = f[m:] + [0]*m
        butterfly(f)
        for i in range(2*m):
            f[i] = f[i] * g[i] % mod
        butterfly_inv(f)
        iz = pow(2*m, mod-2, mod)
        iz = (-iz*iz) % mod
        for i in range(m):
            f[i] = f[i] * iz % mod
        res += f[:m]
        m <<= 1
    return res[:n]

def log(a):
    a = a.copy()
    n = len(a)
    assert n > 0 and a[0] == 1
    a_inv = inverse(a)
    a=differentiate(a)
    a = convolution(a, a_inv)[:n]
    a=integrate(a)
    return a

def exp(a):
    a = a.copy()
    n = len(a)
    assert n > 0 and a[0] == 0
    g = [1]
    a[0] = 1
    h_drv = a.copy()
    h_drv=differentiate(h_drv)
    m = 1
    while m < n:
        f_fft = a[:m] + [0] * m
        butterfly(f_fft)

        if m > 1:
            _f = [f_fft[i] * g_fft[i] % mod for i in range(m)]
            butterfly_inv(_f)
            _f = _f[m // 2:] + [0] * (m // 2)
            butterfly(_f)
            for i in range(m):
                _f[i] = _f[i] * g_fft[i] % mod
            butterfly_inv(_f)
            _f = _f[:m//2]
            iz = pow(m, mod - 2, mod)
            iz *= -iz
            iz %= mod
            for i in range(m//2):
                _f[i] = _f[i] * iz % mod
            g.extend(_f)

        t = a[:m]
        t=differentiate(t)
        r = h_drv[:m - 1]
        r.append(0)
        butterfly(r)
        for i in range(m):
            r[i] = r[i] * f_fft[i] % mod
        butterfly_inv(r)
        im = pow(-m, mod - 2, mod)
        for i in range(m):
            r[i] = r[i] * im % mod
        for i in range(m):
            t[i] = (t[i] + r[i]) % mod
        t = [t[-1]] + t[:-1]

        t += [0] * m
        butterfly(t)
        g_fft = g + [0] * (2 * m - len(g))
        butterfly(g_fft)
        for i in range(2 * m):
            t[i] = t[i] * g_fft[i] % mod
        butterfly_inv(t)
        t = t[:m]
        i2m = pow(2 * m, mod - 2, mod)
        for i in range(m):
            t[i] = t[i] * i2m % mod
    
        v = a[m:min(n, 2 * m)]
        v += [0] * (m - len(v))
        t = [0] * (m - 1) + t + [0]
        t=integrate(t)
        for i in range(m):
            v[i] = (v[i] - t[m + i]) % mod

        v += [0] * m
        butterfly(v)
        for i in range(2 * m):
            v[i] = v[i] * f_fft[i] % mod
        butterfly_inv(v)
        v = v[:m]
        i2m = pow(2 * m, mod - 2, mod)
        for i in range(m):
            v[i] = v[i] * i2m % mod
        
        for i in range(min(n - m, m)):
            a[m + i] = v[i]
        
        m *= 2
    return a

def power(a,k):
    n = len(a)
    assert n>0
    if k==0:
        return [1]+[0]*(n-1)
    l = 0
    while l < len(a) and not a[l]:
        l += 1
    if l * k >= n:
        return [0] * n
    ic = pow(a[l], mod - 2, mod)
    pc = pow(a[l], k, mod)
    a = log([a[i] * ic % mod for i in range(l, len(a))])
    for i in range(len(a)):
        a[i] = a[i] * k % mod
    a = exp(a)
    for i in range(len(a)):
        a[i] = a[i] * pc % mod
    a = [0] * (l * k) + a[:n - l * k]
    return a

def sqrt(a):
    if len(a) == 0:
        return []
    if a[0] == 0:
        for d in range(1, len(a)):
            if a[d]:
                if d & 1:
                    return None
                if len(a) - 1 < d // 2:
                    break
                res=sqrt(a[d:]+[0]*(d//2))
                if res == None:
                    return None
                res = [0]*(d//2)+res
                return res
        return [0]*len(a)
    
    sqr = Tonelli_Shanks(a[0],mod)
    if sqr == None:
        return None
    T = [0] * (len(a))
    T[0] = sqr
    res = T.copy()
    T[0] = pow(sqr,mod-2,mod) #T:res^{-1}
    m = 1
    two_inv = (mod + 1) // 2
    F = [sqr]
    while m <= len(a) - 1:
        for i in range(m):
            F[i] *= F[i]
            F[i] %= mod
        butterfly_inv(F)
        iz = pow(m, mod-2, mod)
        for i in range(m):
            F[i] = F[i] * iz % mod
        delta = [0] * (2 * m)
        for i in range(m):
            delta[i + m] = F[i] - a[i] - (a[i + m] if i+m<len(a) else 0)
        butterfly(delta)
        G = [0] * (2 * m)
        for i in range(m):
            G[i] = T[i]
        butterfly(G)
        for i in range(2 * m):
            delta[i] *= G[i]
            delta[i] %= mod
        butterfly_inv(delta)
        iz = pow(2*m, mod-2, mod)
        for i in range(2*m):
            delta[i] = delta[i] * iz % mod
        for i in range(m, min(2 * m, len(a))):
            res[i] = -delta[i] * two_inv%mod
            res[i]%=mod
        if 2 * m > len(a) - 1:
            break
        F = res[:2 * m]
        butterfly(F)
        eps = [F[i] * G[i] % mod for i in range(2 * m)]
        butterfly_inv(eps)
        for i in range(m):
            eps[i] = 0
        iz = pow(2*m, mod-2, mod)
        for i in range(m,2*m):
            eps[i] = eps[i] * iz % mod
        butterfly(eps)
        for i in range(2 * m):
            eps[i] *= G[i]
            eps[i] %= mod
        butterfly_inv(eps)
        for i in range(m, 2 * m):
            T[i] = -eps[i]*iz
            T[i]%=mod
        iz = iz*iz % mod
        m <<= 1
    return res

def division_modulus(f,g):
    n=len(f)
    m=len(g)
    while m and g[m-1]==0:
        m-=1
    assert m
    if n>=m:
        fR=f[::-1][:n-m+1]
        gR=g[:m][::-1][:n-m+1]+[0]*max(0,n-m+1-m)
        qR=convolution(fR,inverse(gR))[:n-m+1]
        q=qR[::-1]
        r=[(f[i]-x)%mod for i,x in enumerate(convolution(g,q)[:m-1])]
        while r and r[-1]==0:
            r.pop()
    else:
        q,r=[],f.copy()
    return q,r

def taylor_shift(a,c):
    a=a.copy()
    n=len(a)
    #MD=MOD(mod)
    #MD.Build_Fact(n-1)
    for i in range(n):
        a[i]*=MD.Fact(i)
        a[i]%=mod
    C=[1]
    for i in range(1,n):
        C.append(C[-1]*c%mod)
    for i in range(n):
        C[i]*=MD.Fact_Inve(i)
        C[i]%=mod
    a=convolution(a,C[::-1])[n-1:]
    for i in range(n):
        a[i]*=MD.Fact_Inve(i)
        a[i]%=mod
    return a

def multipoint_evaluation(f, x):
    n = len(x)
    sz = 1 << (n - 1).bit_length()
    g = [[1] for _ in range(2 * sz)]
    for i in range(n):
        g[i + sz] = [-x[i], 1]
    for i in range(1, sz)[::-1]:
        g[i] = convolution(g[2 * i],g[2 * i + 1])
    g[1] =division_modulus(f,g[1])[1]
    for i in range(2, 2 * sz):
        g[i]=division_modulus(g[i>>1],g[i])[1]
    res = [g[i + sz][0] if g[i+sz] else 0 for i in range(n)]
    return res

def Chirp_Z_transform(f,q,M):
    if q==0:
        if f:
            return f[0]%mod
        else:
            return 0
    if M==0:
        return []
    N=len(f)
    pow_q=[1]+[q]*(N+M-2)
    inve_q=pow(q,mod-2,mod)
    pow_inve_q=[1]+[inve_q]*(N+M-2)
    for _ in range(2):
        for i in range(1,N+M-1):
            pow_q[i]*=pow_q[i-1]
            pow_q[i]%=mod
            pow_inve_q[i]*=pow_inve_q[i-1]
            pow_inve_q[i]%=mod
    a=[f[i]*pow_inve_q[i]%mod for i in range(N-1,-1,-1)]
    b=pow_q
    ab=convolution(a,b)
    return [ab[j+N-1]*pow_inve_q[j]%mod for j in range(M)]

def relaxed_convolution(N,f):
    retu=[0]*N
    A,B=[],[]
    C=None
    for i in range(N):
        a,b=f(i,C)
        A.append(a)
        B.append(b)
        pow2=1
        while (i+2)%pow2==0:
            if pow2==i+2:
                break
            elif pow2*2==i+2:
                tpl=((i+1-pow2,i+1,i+1-pow2,i+1),)
            else:
                tpl=((pow2-1,2*pow2-1,i+1-pow2,i+1),(i+1-pow2,i+1,pow2-1,2*pow2-1),)
            for la,ra,lb,rb in tpl:
                for j,c in enumerate(convolution(A[la:ra],B[lb:rb]),la+lb):
                    if j<N:
                        retu[j]+=c
                        retu[j]%=mod
            pow2*=2
        C=retu[i]
    return retu

def Berlekamp_Massey(A,mod):
    n = len(A)
    B, C = [1], [1]
    l, m, p = 0, 1, 1
    for i in range(n):
        d = A[i]
        for j in range(1, l + 1):
            d += C[j] * A[i - j]
            d %= mod
        if d == 0:
            m += 1
            continue
        T = C.copy()
        q = pow(p, mod - 2, mod) * d % mod
        if len(C) < len(B) + m:
            C += [0] * (len(B) + m - len(C))
        for j, b in enumerate(B):
            C[j + m] -= q * b
            C[j + m] %= mod
        if 2 * l <= i:
            B = T
            l, m, p = i + 1 - l, 1, d
        else:
            m += 1
    res = [-c % mod for c in C[1:]]
    return res

def BMBM(A,N,mod):
    deno=[1]+[-c for c in Berlekamp_Massey(A,mod)]
    nume=[0]*(len(deno)-1)
    for i in range(len(A)):
        for j in range(len(deno)):
            if i+j<len(nume):
                nume[i+j]+=A[i]*deno[j]
                nume[i+j]%=mod
    return Bostan_Mori(nume,deno,N,mod=mod)













import math
from collections import defaultdict

# pow/log/exp of FPS
# thanks for https://judge.yosupo.jp/submission/126665

# FFT
# code from: https://atcoder.jp/contests/practice2/submissions/24974537
# but changed a little
_fft_mod = 998244353
_fft_imag = 911660635
_fft_iimag = 86583718
_fft_rate2 = (911660635, 509520358, 369330050, 332049552, 983190778, 123842337, 238493703, 975955924, 603855026, 856644456, 131300601, 842657263, 730768835, 942482514, 806263778, 151565301, 510815449, 503497456, 743006876, 741047443, 56250497, 867605899)
_fft_irate2 = (86583718, 372528824, 373294451, 645684063, 112220581, 692852209, 155456985, 797128860, 90816748, 860285882, 927414960, 354738543, 109331171, 293255632, 535113200, 308540755, 121186627, 608385704, 438932459, 359477183, 824071951, 103369235)
_fft_rate3 = (372528824, 337190230, 454590761, 816400692, 578227951, 180142363, 83780245, 6597683, 70046822, 623238099,  183021267, 402682409, 631680428, 344509872, 689220186, 365017329, 774342554, 729444058, 102986190, 128751033, 395565204)
_fft_irate3 = (509520358, 929031873, 170256584, 839780419, 282974284, 395914482, 444904435, 72135471, 638914820, 66769500, 771127074, 985925487, 262319669, 262341272, 625870173, 768022760, 859816005, 914661783, 430819711, 272774365, 530924681)

def _butterfly(a):
	n = len(a)
	h = (n - 1).bit_length()
	len_ = 0
	while len_ < h:
		if h - len_ == 1:
			p = 1 << (h - len_ - 1)
			rot = 1
			for s in range(1 << len_):
				offset = s << (h - len_)
				for i in range(p):
					l = a[i + offset]
					r = a[i + offset + p] * rot % _fft_mod
					a[i + offset] = (l + r) % _fft_mod
					a[i + offset + p] = (l - r) % _fft_mod
				if s + 1 != (1 << len_):
					rot *= _fft_rate2[(~s & -~s).bit_length() - 1]
					rot %= _fft_mod
			len_ += 1
		else:
			p = 1 << (h - len_ - 2)
			rot = 1
			for s in range(1 << len_):
				rot2 = rot * rot % _fft_mod
				rot3 = rot2 * rot % _fft_mod
				offset = s << (h - len_)
				for i in range(p):
					a0 = a[i + offset]
					a1 = a[i + offset + p] * rot
					a2 = a[i + offset + p * 2] * rot2
					a3 = a[i + offset + p * 3] * rot3
					a1na3imag = (a1 - a3) % _fft_mod * _fft_imag
					a[i + offset] = (a0 + a2 + a1 + a3) % _fft_mod
					a[i + offset + p] = (a0 + a2 - a1 - a3) % _fft_mod
					a[i + offset + p * 2] = (a0 - a2 + a1na3imag) % _fft_mod
					a[i + offset + p * 3] = (a0 - a2 - a1na3imag) % _fft_mod
				if s + 1 != (1 << len_):
					rot *= _fft_rate3[(~s & -~s).bit_length() - 1]
					rot %= _fft_mod
			len_ += 2
 
def _butterfly_inv(a):
	n = len(a)
	h = (n - 1).bit_length()
	len_ = h
	while len_:
		if len_ == 1:
			p = 1 << (h - len_)
			irot = 1
			for 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) % _fft_mod
					a[i + offset + p] = (l - r) * irot % _fft_mod
				if s + 1 != (1 << (len_ - 1)):
					irot *= _fft_irate2[(~s & -~s).bit_length() - 1]
					irot %= _fft_mod
			len_ -= 1
		else:
			p = 1 << (h - len_)
			irot = 1
			for s in range(1 << (len_ - 2)):
				irot2 = irot * irot % _fft_mod
				irot3 = irot2 * irot % _fft_mod
				offset = s << (h - len_ + 2)
				for i in range(p):
					a0 = a[i + offset]
					a1 = a[i + offset + p]
					a2 = a[i + offset + p * 2]
					a3 = a[i + offset + p * 3]
					a2na3iimag = (a2 - a3) * _fft_iimag % _fft_mod
					a[i + offset] = (a0 + a1 + a2 + a3) % _fft_mod
					a[i + offset + p] = (a0 - a1 +
										 a2na3iimag) * irot % _fft_mod
					a[i + offset + p * 2] = (a0 + a1 -
											 a2 - a3) * irot2 % _fft_mod
					a[i + offset + p * 3] = (a0 - a1 -
											 a2na3iimag) * irot3 % _fft_mod
				if s + 1 != (1 << (len_ - 1)):
					irot *= _fft_irate3[(~s & -~s).bit_length() - 1]
					irot %= _fft_mod
			len_ -= 2
 
def _convolution_naive(a, b):
	n = len(a)
	m = len(b)
	ans = [0] * (n + m - 1)
	if n < m:
		for j in range(m):
			for i in range(n):
				ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
	else:
		for i in range(n):
			for j in range(m):
				ans[i + j] = (ans[i + j] + a[i] * b[j]) % _fft_mod
	return ans
 
def _convolution_fft(a, b):
	a = a.copy()
	b = b.copy()
	n = len(a)
	m = len(b)
	z = 1 << (n + m - 2).bit_length()
	a += [0] * (z - n)
	_butterfly(a)
	b += [0] * (z - m)
	_butterfly(b)
	for i in range(z):
		a[i] = a[i] * b[i] % _fft_mod
	_butterfly_inv(a)
	a = a[:n + m - 1]
	iz = pow(z, _fft_mod - 2, _fft_mod)
	for i in range(n + m - 1):
		a[i] = a[i] * iz % _fft_mod
	return a
 
 
def _convolution_square(a):
	a = a.copy()
	n = len(a)
	z = 1 << (2 * n - 2).bit_length()
	a += [0] * (z - n)
	_butterfly(a)
	for i in range(z):
		a[i] = a[i] * a[i] % _fft_mod
	_butterfly_inv(a)
	a = a[:2 * n - 1]
	iz = pow(z, _fft_mod - 2, _fft_mod)
	for i in range(2 * n - 1):
		a[i] = a[i] * iz % _fft_mod
	return a
 
 
def convolution(a, b):
	n = len(a)
	m = len(b)
	if n == 0 or m == 0:
		return []
	if min(n, m) <= 0:
		return _convolution_naive(a, b)
	if a is b:
		return _convolution_square(a)
	return _convolution_fft(a, b)
# ----

# 1/F
# 必要 : a[0] != 0
# 前提 : FFT
def poly_inv(a, length = None):
	if length == None: M = len(a)
	else: M = length
	if M <= 0: return []
	n = len(a)
	r = pow(a[0], _fft_mod-2, _fft_mod)
	m = 1
	res = [r]
	while m < M:
		f = a[:min(n,2*m)] + [0]*(2*m-min(n,2*m))
		g = res + [0]*m
		_butterfly(f)
		_butterfly(g)
		for i in range(2*m):
			f[i] = f[i] * g[i] % _fft_mod
		_butterfly_inv(f)
		f = f[m:] + [0]*m
		_butterfly(f)
		for i in range(2*m):
			f[i] = f[i] * g[i] % _fft_mod
		_butterfly_inv(f)
		iz = pow(2*m, _fft_mod-2, _fft_mod)
		iz = (-iz*iz) % _fft_mod
		for i in range(m):
			f[i] = f[i] * iz % _fft_mod
		res += f[:m]
		m <<= 1
	return res[:M]

# 多点評価
# x に評価したい点を配列で入れよう！
def multi_eval(x, a):
	n = len(x)
	siz = 1 << (n-1).bit_length()

	g = [[1] for i in range(2 * siz)]

	for i in range(n):
		g[i + siz] = [-x[i], 1]

	for i in range(siz-1, 0, -1):
		g[i] = convolution(g[2 * i], g[2 * i + 1])
	
	for i in range(1, 2 * siz):
		if i == 1: f = a[::]
		else: f = g[i >> 1]
		m = len(f) - len(g[i]) + 1
		v = convolution(f[::-1][:m], poly_inv(g[i][::-1], m))[m-1::-1]
		w = convolution(v, g[i])
		g[i] = f[::]
		h = g[i]

		for j in range(len(w)):
			h[j] -= w[j]
			h[j] %= _fft_mod
		
		while len(h) > 1 and h[-1] == 0:
			h.pop()
	
	return [g[i+siz][0] for i in range(n)]


# DEF MOD FACT
mod = _fft_mod
N = 10**6 + 5
fact = [1]*(N+1)
factinv = [1]*(N+1)

for i in range(2, N+1):
	fact[i] = fact[i-1] * i % mod

factinv[-1] = pow(fact[-1], mod-2, mod)
for i in range(N-1, 1, -1):
	factinv[i] = factinv[i+1] * (i+1) % mod

def cmb(a, b):
	if (a < b) or (b < 0): return 0
	return fact[a] * factinv[b] % mod * factinv[a-b] % mod

# log(F)
# 必要 : a[0] = 1
# 前提 : FFT, inv
def poly_log(a, length = None):
	if length == None: M = len(a)
	else: M = length
	if M <= 0: return []
	n = len(a)
	if n == 1: return [0] * M
	b = [a[i+1] * (i+1) % _fft_mod for i in range(n-1)]
	t = convolution(b, poly_inv(a, length = M))
	return [0] + [t[i] * factinv[i+1] % _fft_mod * fact[i] % _fft_mod for i in range(M-1)]

# exp(F)
# 必要 : a[0] = 0
# 前提 : FFT, inv, log
def poly_exp(a, length = None):
	if length == None: M = len(a)
	else: M = length
	if M <= 0: return []
	n = len(a)
	m = 1
	res = [1]
	while m < M:
		f = a[:min(n,2*m)] + [0]*(2*m-min(n,2*m))
		#print(res)
		v = poly_log(res, length = 2*m)
		w = [(f[i]-v[i])%_fft_mod for i in range(2*m)]
		w[0] = (w[0]+1)%_fft_mod
		g = convolution(res, w)
		res += g[m:2*m]
		m <<= 1
	return res[:M]

def poly_pow_nonzero(a, m, l):
	n = len(a)
	bais = pow(a[0], m, _fft_mod)
	invs = pow(a[0], _fft_mod-2, _fft_mod)
	r = [a[i] * invs % _fft_mod for i in range(n)]
	r = poly_log(r, length = l)
	for i in range(l):
		r[i] = r[i] * m % _fft_mod
	r = poly_exp(r, length = l)
	for i in range(l):
		r[i] = r[i] * bais % _fft_mod
	return r


def poly_pow(a, m, l):
	n = len(a)
	ind = 0
	for i in range(n):
		if a[i] != 0:
			ind = i
			break
	if ind * m >= l:
		return [0] * l
	return [0] * (ind * m) + poly_pow_nonzero(a[ind:], m, l-ind*m)

# DEF MOD FACT はされています！！6







N,K=map(int,input().split())
A=list(map(int,input().split()))
mod=998244353
MOD=998244353

facts = [1] * (K + 1)
ifacts = [1] * (K + 1)
for i in range(K):
    facts[i + 1] = facts[i] * (i + 1) % MOD
    ifacts[i + 1] = pow(facts[i + 1], MOD - 2, MOD)

F = [[0 for i in range(K + 1)] for j in range(K + 1)]
F_log = [[0 for i in range(K + 1)] for j in range(K + 1)]

for i in range(K + 1):
    for j in range(i + 1):
        F[i][j] = ifacts[j]
    F_log[i] = poly_log(F[i])
memo_log=F_log
ans=0
cntD=[0]*(K+1)
for d in range(K):
    cntD[math.gcd(K,d)]+=1
for d in range(K+1):
    if cntD[d]:
        S=K//d
        cnt=[0]*(d+2)
        for i in range(N):
            cnt[min(d,A[i]//S)]+=1
        poly=exp([sum(memo_log[c][x]*cnt[c]%mod for c in range(1,d+1)) for x in range(d+1)])
        ans+=cntD[d]*poly[d]%mod*fact[d]%mod
        ans%=mod
ans*=pow(K,mod-2,mod)
ans%=mod
print(ans)