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 math

def kp(n):
    return (n*n+n)/2
def tc():
    return map(int,raw_input().split())

for _ in range(input()):
    n,x=tc()
    a=tc()
    ans=0
    ok=1
    while a!=sorted(a):
        p=sorted(a+[x])
        tp=[]
        for i in range(n+1):
            if p[i]==x:
                tp.append(i)
        if tp[-1]==n:
            if a==sorted(a):
                print ans
            else:
                print -1
            ok=0
            break
        m=float('inf')
        pc=-1
        tk=1
        for i in range(len(tp)):
            if tp[i]!=n and a[tp[i]]<x :
                tk=0;print-1;break
            if a[tp[i]]<m and a[tp[i]]>x:
                m=a[tp[i]];pc=tp[i]
        if tk==0:
            ok=0;break
        if a[pc]<=x:
            ok=0;print -1;break
        ans+=1;a[pc],x=x,a[pc]
      
    if ok:
        print ans
        
            
            
        