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
for i in range(int(input())):
    n,x = map(int,input().split(" "))
    l = list(map(int,input().split(" ")))

    if n == 1 : 
        print(0)
    else:
        c = 1
        count = 0
        for i in range(1,n):
            if l[i] >= l[i-1]:
                c += 1
        
        if(c == n ):
            print(0)
        else:
            end = False
            for i in range(0,n):
                if end:
                    i = n
                    continue
                if l[i] > x:
                    # print(l,x)
                    x,l[i] = l[i],x
                    count += 1
                    # print(l,x,count)

                    c = 1
                    for i in range(1,n):
                        if l[i] >= l[i-1]:
                            c += 1
                    
                    if(not c == n):
                        continue
                    else:                        
                        print(count)
                        end =True

            if not end :
                c = 1
                for i in range(1,n):
                    if l[i] >= l[i-1]:
                        c += 1
                
                if(c == n ):
                    print(count)
                else:
                    print(-1)