You are given an array A. A triplet is said to be a Harmonic triplet if it satisfies the following conditions :

• \(i \lt j \lt k\)
• \(A[i] \le A[j] \ge A[k]\)

You have to find the \(harmonic\) \( triplet\) with the maximum value of \(A[i] \times A[j] \times A[k]\).
You are given q queries, where in each query you are given \(j^{th}\) index and you have to find the \(harmonic\) \(triplet\) with value at \(j^{th}\) index which has maximum product.

Note
If there are no elements to the left or right of j which satisfy the given conditions, answer for the given index will be 0.

Input format

• The first line contains single integer T denoting the number of test cases. T test cases follow.
• The first line of each test case consists of two space-separated integers \(N, Q\) denoting size of the array and number of the queries respectively.
• Next line contains N spaced integers denoting contents of the array.
• The next Q lines contain values of \(j^{th}\) index for which you have to find harmonic triplet with maximum product.

Output format

• For each test case, for each query print a single line consisting of the maximum possible product for that query.

Constraints

• \(1 \le T \le 5\)
• \(1 \le N,Q \le 10^5\)
• \(1 \le A[i] \le 10^5\)
• \(1 \le j \le N\)

Note
Use fast I/O techniques.