import math
from collections import Counter
N,K = map(int,input().split())
A = list(map(int,input().split()))
mod = 998244353
def md(n):
    lower_divisors , upper_divisors = [], []
    i = 1
    while i*i <= n:
        if n % i == 0:
            lower_divisors.append(i)
            if i != n // i:
                upper_divisors.append(n//i)
        i += 1
    return lower_divisors + upper_divisors[::-1]
    
class combination():
    
    def __init__(self,N,p):
        
        
        self.fact = [1, 1]  # fact[n] = (n! mod p)
        self.factinv = [1, 1]  # factinv[n] = ((n!)^(-1) mod p)
        self.inv = [0, 1]  # factinv 計算用
        self.p = p
        
        for i in range(2, N + 1):
            self.fact.append((self.fact[-1] * i) % p)
            self.inv.append((-self.inv[p % i] * (p // i)) % p)
            self.factinv.append((self.factinv[-1] * self.inv[-1]) % p)
        

    def cmb(self,n, r):
        if (r < 0) or (n < r):
            return 0
        r = min(r, n - r)
        return self.fact[n] * self.factinv[r] * self.factinv[n-r] % self.p    
C = combination(3*10**5,mod)
P = md(K)
n = len(P)
P.sort()
inv = {p:i for i,p in enumerate(P)}
A = [math.gcd(a,K) for a in A]
T = Counter(A)
N = len(T)
dp = [[0]*n for _ in range(len(T)+1)]
dp[0][0] = 1


idx = 0
for k,v in T.items():
    
    
    for j in range(n-1,-1,-1):
        p = P[j]
        res = 1
        for _ in range(v,-1,-1):
            jdx = inv[math.gcd(p*res,K)]
            dp[idx+1][jdx] = (dp[idx+1][jdx] + dp[idx][inv[p]]*C.cmb(v,_))%mod
            res = math.gcd(res*k,K)
    idx += 1
print(dp[-1][-1])