Eva loves numbers. She has a list A of n distinct numbers containing numbers A₁,A₂....,A_n. She wants to get more numbers, so she decided to create a new list B. 

As she wants to get more numbers, she decides to copy numbers from list A to list B in a weird way :

• She picks numbers from list A one by one from A₁ to A_n.   
• She picks an element A_i (1 < i < n) from list A, copies that element in list B.
• Then, she copies all the numbers from list A valued between A_i and 2*A_i (inclusive) to list B.

Now, she has a lot of numbers in list B and Zan is interested in her new list B.

He ask her some queries. In each query, he gives her a number x, Eva has to answer that how many elements are greater than x in her new list B.

As, she has already done a lot of work in creating list B. You have to answer queries for her.

Example:

If she has list A = {1,2,3,4} and B = { }.

For A₁,A₂,...,A₄:

• She picks A₁ = 1.
• She copies A₁ to B. Now, B = {1}.
• She picks all the numbers from list A valued between A_i and 2*A_i, and copies them to list B. Now, B = {1,1,2}.
• Repeat for A₂,...,A₄.

 The final list B = {1,1,2,2,2,3,3,3,4,4,4,4}.

Input

The first line contains an integer t (1 ≤ t ≤ 10²) — the number of test cases in the input. Then t test cases follow.

The first line contains two positive integers n,q (1 ≤ n ,q ≤ 10⁴) — length of the list A and number of the queries respectively.

The second line contains n positive integers A₁,A₂,…,A_n ( 0 ≤ A_i ≤ 10⁴ ), where A_i is the  i-th element of the list A .

Next q lines contains an integer x (0 < x < 10⁴).

Output

You have to ouput answer for each query - the number of elements greater than x in the list B.