Sequence and Swaps

You are given a sequence a consisting of n integers a_1, a_2, ..., a_n, and an integer x. Your task is to make the sequence a sorted (it is considered sorted if the condition a_1 ≤ a_2 ≤ a_3 ≤ ... ≤ a_n holds).

To make the sequence sorted, you may perform the following operation any number of times you want (possibly zero): choose an integer i such that 1 ≤ i ≤ n and a_i > x, and swap the values of a_i and x.

For example, if a = [0, 2, 3, 5, 4], x = 1, the following sequence of operations is possible:

1. choose i = 2 (it is possible since a_2 > x), then a = [0, 1, 3, 5, 4], x = 2;
2. choose i = 3 (it is possible since a_3 > x), then a = [0, 1, 2, 5, 4], x = 3;
3. choose i = 4 (it is possible since a_4 > x), then a = [0, 1, 2, 3, 4], x = 5.

Calculate the minimum number of operations you have to perform so that a becomes sorted, or report that it is impossible.

Input

The first line contains one integer t (1 ≤ t ≤ 500) — the number of test cases.

Each test case consists of two lines. The first line contains two integers n and x (1 ≤ n ≤ 500, 0 ≤ x ≤ 500) — the number of elements in the sequence and the initial value of x.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 500).

The sum of values of n over all test cases in the input does not exceed 500.

Output

For each test case, print one integer — the minimum number of operations you have to perform to make a sorted, or -1, if it is impossible.

Example

Input

6 4 1 2 3 5 4 5 6 1 1 3 4 4 1 10 2 2 10 11 9 2 10 12 11 5 18 81 324 218 413 324

Output

3 0 0 -1 1 3

inputFormat

Input

The first line contains one integer t (1 ≤ t ≤ 500) — the number of test cases.

Each test case consists of two lines. The first line contains two integers n and x (1 ≤ n ≤ 500, 0 ≤ x ≤ 500) — the number of elements in the sequence and the initial value of x.

The second line contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 500).

The sum of values of n over all test cases in the input does not exceed 500.

outputFormat

Output

For each test case, print one integer — the minimum number of operations you have to perform to make a sorted, or -1, if it is impossible.

Example

Input

6 4 1 2 3 5 4 5 6 1 1 3 4 4 1 10 2 2 10 11 9 2 10 12 11 5 18 81 324 218 413 324

Output

3 0 0 -1 1 3

样例

6
4 1
2 3 5 4
5 6
1 1 3 4 4
1 10
2
2 10
11 9
2 10
12 11
5 18
81 324 218 413 324

3
0
0
-1
1
3

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