Problem: Today Pari and Arya are playing a game called Remainders.

Pari chooses two positive integer x and k, and tells Arya k but not x. Arya have to find the value <image>. There are n ancient numbers c1, c2, ..., cn and Pari has to tell Arya <image> if Arya wants. Given k and the ancient values, tell us if Arya has a winning strategy independent of value of x or not. Formally, is it true that Arya can understand the value <image> for any positive integer x?

Note, that <image> means the remainder of x after dividing it by y.

Input

The first line of the input contains two integers n and k (1 ≤ n, k ≤ 1 000 000) — the number of ancient integers and value k that is chosen by Pari.

The second line contains n integers c1, c2, ..., cn (1 ≤ ci ≤ 1 000 000).

Output

Print "Yes" (without quotes) if Arya has a winning strategy independent of value of x, or "No" (without quotes) otherwise.

Examples

Input

4 5
2 3 5 12


Output

Yes


Input

2 7
2 3


Output

No

Note

In the first sample, Arya can understand <image> because 5 is one of the ancient numbers.

In the second sample, Arya can't be sure what <image> is. For example 1 and 7 have the same remainders after dividing by 2 and 3, but they differ in remainders after dividing by 7.

Solution (in PYTHON3):

Solution:
import sys
ints = (int(x) for x in sys.stdin.read().split())

def sieve(N):
  n = int((N**.5)+100)
  is_prime = [1]*n
  primes = []
  div = [i for i in range(n)]
  for i in (i for i in range(2, n) if is_prime[i]):
    for j in range(i*i, n, i):
      is_prime[j] = 0
      div[j] = i
    div[i] = i
    primes.append(i)
  return primes, div

from collections import Counter
from itertools import takewhile

def decompose(x, primes, div):
  divs = []
  push = lambda p: divs.append(p) or x//p
  for p in takewhile(lambda p: x>=len(div), primes):
    while x%p==0: x = push(p)
  if x>=len(div): x = push(x)
  while x>1: x = push(div[x])
  return Counter(divs)

primes, div = sieve(10**9)
n, k = next(ints), next(ints)
k = set(a**b for a, b in decompose(k, primes, div).items())
c = set(next(ints) for i in range(n))
print('YES' if all(any(x%y==0 for x in c) for y in k) else 'NO')