Integral Array

Description:

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.

Sample Input:

4
3 5
1 2 5
4 10
1 3 3 7
1 2
2
1 1
1

Sample Output:

Yes
No
No
Yes

Sample Input:

1
1 1000000
1000000

Sample Output:

No

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.