# 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=[min(K,int(x)) for x in input().split()] M=998244353 fa=[1,1] fb=[1,1] for i in range(2,10**4+1): fa+=[fa[-1]*i%M] fb+=[fb[-1]*(M//i)*fb[M%i]*fa[M%i-1]*(-1)%M] fc=lambda n,k:fa[n]*fb[k]*fb[n-k]%M if n>=k>=0 else 0 q2=[] q3=[0]*(K+1) for j in range(K+1): q3[j]=fb[j] q2+=[poly_log(q3)] g=[0]*(K+1) for i in range(1,K+1): if K%i==0: c=[0]*(K+1) for v in a: c[v//(K//i)]+=1 q=[0]*(i+1) for j in range(1,i+1): if c[j]>0: for k in range(i+1): if k<len(q2[j]): q[k]+=q2[j][k]*c[j] q[k]%=M q=poly_exp(q) g[i]=q[i]*fa[i]%M ans=0 from math import gcd for i in range(K): ans+=g[gcd(i,K)] ans%=M print(ans*pow(K,M-2,M)%M)