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


# i misunderstood the problem in the previous submissions

tests_n = int(raw_input())
tests = []
for i in range(tests_n):
    n, initial_x = [int(i) for  i in raw_input().split(' ')]
    array = [int(i) for i in raw_input().split(' ')]

    tests.append([n, initial_x, array])


for test in tests:

    n, x, array = test
    min_approaches = 0
    STSI = 0 if array[0] > x else -1 # Sequence Transform Starting Index
    possible = True
    
    if n == 1:
        print 0
        continue

    if array[0] > array[1]:
        if x <= array[1]:
            min_approaches += 1
            x, array[0] = [array[0], x]
            STSI = -1
        else:
            print -1
            continue 

    for i in range(1, n-1):

        if array[i] > array[i+1]:

            if array[i-1] <= x and x <= array[i+1]:
                min_approaches += 1
                array[i], x = [x, array[i]]
                STSI = -1

            else:
                if STSI == -1:
                    possible = False
                    break
                else:

                    if array[i-1] != array[i] and array[i-1] <= array[i+1]:
                        min_approaches += len(set(array[STSI: i+1]))
                        x, array[i], STSI = [array[i], array[i-1], -1]
                    else:
                        possible = False
                        break

        if array[i] > x and STSI == -1:
            STSI = i

        
    print min_approaches if possible else -1

