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Search in a Rotated Array

Given a sorted and rotated array (rotated at some point) A[ ], and given an element K, the task is to find the index of the given element K in the array A[ ]. The array has no duplicate elements. If the element does not exist in the array, print -1.
 

Input:
The first line of the input contains an integer T, depicting the total number of test cases. Then T test cases follow. Each test case consists of three lines. First line of each test case contains an integer N denoting the size of the given array. Second line of each test case contains N space separated integers denoting the elements of the array A[ ]. Third line of each test case contains an integer K denoting the element to be searched in the array.


Output:

Corresponding to each test case, print in a new line, the index of the element found in the array.  If element is not present, then print -1.


Constraints:

1 ≤ T ≤ 100
1 ≤ N ≤ 100005
0 ≤ A[i] ≤ 10000005
1 ≤ k ≤ 100005


Example:

Input
3
9
5 6 7 8 9 10 1 2 3
10
3
3 1 2
1
4
3 5 1 2
6


Output
5
1
-1

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

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