B. Integral Arraytime limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou 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.InputThe 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.OutputFor each test case print Yes if the array is integral and No otherwise.ExamplesInput
4
3 5
1 2 5
4 10
1 3 3 7
1 2
2
1 1
1
Output
Yes
No
No
Yes
Input
1
1 1000000
1000000
Output
No
NoteIn 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.
4
3 5
1 2 5
4 10
1 3 3 7
1 2
2
1 1
1

Yes No No Yes 
['brute force', 'constructive algorithms', 'data structures', 'math', '*1800']