Given an array $a$ of length $n$, which is a permutation of the integers $0,1,\ldots,n-1$, you can perform the following operation at most once:

• Choose two distinct indices $i$ and $j$ ($i \ne j$), and swap the values of $a_i$ and $a_j$.

After performing the operation, define $f_i=\operatorname{mex}(a_1, a_2, \ldots, a_i)$. $\operatorname{mex}(c)$ denotes the minimum excluded (MEX)$^{\text{∗}}$ of the collection $c$.

Given an integer $k$, find two indices to use in the operation above so as to maximize the $k$-th largest value among $f_1, f_2, \ldots, f_n$. If no operation is needed, output $-1$.

If there are several valid answers, you may output any of them.

$^{\text{∗}}$The minimum excluded (MEX) of a collection of integers $c_1, c_2, \ldots, c_k$ is defined as the smallest non-negative integer $x$ which does not occur in the collection $c$.

Input

Each test contains multiple test cases. The first line contains the number of test cases $t$ ($1 \le t \le 50$). The description of the test cases follows.

For each test case, the first line contains two integers $n$ and $k$ ($2 \le n \le 100$, $1 \le k \le n$), where $n$ is the number of elements in the array $a$ and $k$ is the rank of the value to be maximized (with $k=1$ corresponding to the largest value).

The next line contains $n$ integers: $a_1,a_2,\ldots,a_n$. It is guaranteed that each of the values $0,1,\ldots,n−1$ appears exactly once in the array $a$.

It is guaranteed that the sum of $n$ over all test cases does not exceed $100$.

Output

For each test case, output a single line that contains two indices used in the operation to maximize the $k$-th largest value among $f_1, f_2, \ldots, f_n$. If no operation is needed, output $-1$.

Note

In the first test case, no operation is needed; the $1$st largest value among $f_1, f_2, \ldots, f_5$ is $f_5=5$. Actually, if we perform the swap operation, no matter which two indices we choose, $f_5$ is always the largest one, with value $5$.

In the second test case, after swapping $a_1$ and $a_3$, we get the array $[1,0,2]$, and $f_1=0, f_2=2, f_3=3$; the $2$nd largest value among $f_1, f_2, f_3$ is $f_2=2$.