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
import sys
#import heapq as hq
#from collections import deque
#sys.stdin = open('in', 'r')
readline = sys.stdin.readline
rdw = lambda: readline().rstrip()
rdws = lambda: readline().split()
rdwl = lambda: list(readline().split())
rdi = lambda: int(readline())
rdis = lambda: map(int, readline().split())
rdil = lambda: list(map(int, readline().split()))
rdilrows = lambda cnt: [rdil() for _ in range(cnt)]

def solve():
    n,x = rdis()
    a = rdil()
    res = 0
    for i in range(n-1):
        if a[i] > a[i+1]:
            if a[i] > x and x <= a[i+1]:
                j = i - 1
                while j >= 0 and a[j] > x:
                    if a[j] > a[i+1]:
                        print(-1)
                        return
                    if a[j] != a[j+1]:
                        res += 1
                    j -= 1
                x = a[i]
                res += 1
            else:
                res = -1
                break
    print(res)


tests = 1
tests = rdi()
for testnum in range(tests):
    solve()
    
#n = rdi()
#n,m = rdis()
#s = rdw()
#a = rdil()
#op, *s = rdws()

#print(f'Case #{testnum+1}: {res}')
#print(*res, sep='\n')
#sys.stdout.write('YES\n')
#sys.stdout.write(f'{res}\n')
#sys.stdout.write(f'{y1} {x1} {y2} {x2}\n')
