Given a sorted array A[]  ( 0 based index ) and a key "k"  you need to complete the function bin_search to  determine the position of the key if the key is present in the array. If the key is not  present then you have to return -1. The arguments left and right denotes the left most index  and right most index of the array A[] .
There are multiple test cases. For each test case, this function will be called individually.

Example

Input:
The first line contains an integer 'T' denoting the number of test cases. Then 'T' test cases follow. Each test case consists of 3 lines. First line of each test case contains an integer N denoting the size of the array . Second line of each test case consists of 'N' space separated integers denoting the elements of the array A[]. The third line contains a key 'k' .

Output:
Prints the position of the key if its present in the array else print -1 if the key is not present in the array.

Constraints:
1<=T<=600
1<=N<=200

Example:
Input:
2
5
1 2 3 4 5 
4
5
11 22 33 44 55
445

Output:
3
-1

** For More Input/Output Examples Use 'Expected Output' option **