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 q11 in range(int(input())):
    n, x = map(int, input().split())
    a = list(map(int, input().split()))
    max1 = max2 = -float('inf')
    for q in range(n):
        if a[q] > max1:
            max2, max1 = max1, a[q]
        elif a[q] > max2:
            max2 = a[q]
        if a[q] < max2:
            print(-1)
            break
    else:
        seg = []
        for q in range(1, n):
            if a[q-1] > a[q]:
                seg.append(q-1)
        if len(seg) == 0:
            print(0)
        elif a[seg[0]+1] < x:
            print(-1)
        else:
            q1, q2, plus = seg[0]-1, 0, 1
            while q1 > -1 and a[q1] > x:
                plus += (q1 == 0 or a[q1] != a[q1-1])
                q1 -= 1
            for q in range(seg[0]+1, seg[-1]+1):
                if q == seg[q2+1]:
                    plus += 1
                    q2 += 1
                else:
                    plus += (a[q] > a[seg[q2]] and a[q] != a[q-1])
            print(plus)
