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
#include <iostream>
#include <vector>

struct Data {
    int32_t x, max, op;
    Data(int32_t x_, int32_t max_, int32_t op_) {
        x = x_;
        max = max_;
        op = op_;
    }
};

int main(int argc, char const *argv[]) {
    int32_t t; std::cin >> t;
    while (t--) {
        int32_t n, x; std::cin >> n >> x;
        std::vector<int32_t> array(n);
        for (int32_t i = 0; i < n; ++i) std::cin >> array[i];
        std::vector<std::vector<Data>> possibleX(n);
        possibleX[0] = {{x, array[0], 0}};
        if (x < array[0]) possibleX[0].push_back({array[0], x, 1});
        for (int32_t i = 1; i < n; i++) {
            for (Data data : possibleX[i - 1]) {
                if (data.max <= array[i]) {
                    possibleX[i].push_back({data.x, array[i], data.op});
                }
                if (data.x < array[i] && data.x >= data.max) {
                    possibleX[i].push_back({array[i], data.x, data.op + 1});
                }
            }
        }
        if (possibleX[n - 1].empty()) {
            std::cout << -1 << std::endl;
        } else {
            int32_t min = 228228;
            for (Data data : possibleX[n - 1]) {
                min = std::min(min, data.op);
            }
            std::cout << min << std::endl;
        }
    }
    return 0;
}
