1455D · Sequence and Swaps

Problem: You 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:

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 Format: The 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 $500$.

Output Format: 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.