The hardest gcd problem GCDDIV

All submissions for this problem are available.<h3>Read problems statements in Mandarin chinese, Russian and Vietnamese as well.</h3>

You are given a sequence $A_1, A_2, \dots, A_N$ of positive integers and an integer $K$. You are allowed to perform the following operation any number of times (including zero):

• choose an index $j$ between $1$ and $N$ inclusive
• choose a positive divisor $d$ of $A_j$ such that $d \le K$
• divide $A_j$ by $d$

Determine if it is possible to modify the sequence $A$ in such a way that it would satisfy the following condition: there is no positive integer strictly greater than $1$ which divides every element of $A$. (In other words, the greatest common divisor of all elements of $A$ should be $1$.)

Input

• The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
• The first line of each test case contains two space-separated integers $N$ and $K$.
• The second line contains $N$ space-separated integers $A_1, A_2, \dots, A_N$.

Output

For each test case, print a single line containing the string "YES" if it is possible to make the GCD of all elements of $A$ equal to $1$ or "NO" if it is impossible.

Constraints

• $1 \le T \le 10$
• $1 \le N \le 10^5$
• $1 \le A_i \le 10^9$ for each valid $i$
• $1 \le K \le 10^9$

Subtasks

Subtask #1 (30 points):

• $1 \le N, K \le 100$
• $1 \le A_i \le 100$ for each valid $i$

Subtask #2 (70 points): original constraints

Example Input

2
3 6
10 15 30
3 4
5 10 20

Example Output

YES
NO