You are given an array $a$ of $n$ positive integers numbered from $1$ to $n$. Let's call an array integral if for any two, not necessarily different, numbers $x$ and $y$ from this array, $x \ge y$, the number $\left \lfloor \frac{x}{y} \right \rfloor$ ($x$ divided by $y$ with rounding down) is also in this array.

You are guaranteed that all numbers in $a$ do not exceed $c$. Your task is to check whether this array is integral.

Input

The input consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. Description of the test cases follows.

The first line of each test case contains two integers $n$ and $c$ ($1 \le n \le 10^6$, $1 \le c \le 10^6$) — the size of $a$ and the limit for the numbers in the array.

The second line of each test case contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($1 \le a_i \le c$) — the array $a$.

Let $N$ be the sum of $n$ over all test cases and $C$ be the sum of $c$ over all test cases. It is guaranteed that $N \le 10^6$ and $C \le 10^6$.

Output

For each test case print Yes if the array is integral and No otherwise.

Note

In the first test case it is easy to see that the array is integral:

• $\left \lfloor \frac{1}{1} \right \rfloor = 1$, $a_1 = 1$, this number occurs in the arry
• $\left \lfloor \frac{2}{2} \right \rfloor = 1$
• $\left \lfloor \frac{5}{5} \right \rfloor = 1$
• $\left \lfloor \frac{2}{1} \right \rfloor = 2$, $a_2 = 2$, this number occurs in the array
• $\left \lfloor \frac{5}{1} \right \rfloor = 5$, $a_3 = 5$, this number occurs in the array
• $\left \lfloor \frac{5}{2} \right \rfloor = 2$, $a_2 = 2$, this number occurs in the array

Thus, the condition is met and the array is integral.

In the second test case it is enough to see that

$\left \lfloor \frac{7}{3} \right \rfloor = \left \lfloor 2\frac{1}{3} \right \rfloor = 2$, this number is not in $a$, that's why it is not integral.

In the third test case $\left \lfloor \frac{2}{2} \right \rfloor = 1$, but there is only $2$ in the array, that's why it is not integral.