D. Sequence and Swapstime limit per test1.5 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputYou are given a sequence a consisting of n integers a_1, a_2, \dots, a_n, and an integer x. Your task is to make the sequence a sorted (it is considered sorted if the condition a_1 \le a_2 \le a_3 \le \dots \le 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 \le i \le 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:  choose i = 2 (it is possible since a_2 > x), then a = [0, 1, 3, 5, 4], x = 2;  choose i = 3 (it is possible since a_3 > x), then a = [0, 1, 2, 5, 4], x = 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.InputThe first line contains one integer t (1 \le t \le 500) — the number of test cases.Each test case consists of two lines. The first line contains two integers n and x (1 \le n \le 500, 0 \le x \le 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 \le a_i \le 500).The sum of values of n over all test cases in the input does not exceed 500.OutputFor 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.ExampleInput
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

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

3 0 0 -1 1 3 
['dp', 'greedy', 'sortings', '*1600']