There are n plants in an array. The beauty of the the i'th plant is a_{i}. We call a contiguous subarray of the plants perfect, iff the GCD of the beauties of the plants in the subarray is x. For example, if the plants in the subarray have beauties [6, 4, 10], the GCD is 2.

Does there exist any perfect contiguous subarray in the array?

Input

The first line has two integers n and x: the number of plants and the required GCD.

The second line contains n integers a_1, a_2,\dots,a_n: The beauties of the plants.

Output

Print YES if there is a subarray whose GCD is x and NO otherwise.

Constraints

• 1 \leq x, n, a_i \leq 10^5

Example 1

Input:

3 2
4 6 7

Output:

YES

Example 2

Input:

3 2
4 7 6

Output:

NO