You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in python3.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```python
<your code here>
```

Execution time limit: 2.0 seconds
Memory limit: 256.0 MB

# Problem
You are given a binary string $$$s$$$ of length $$$n$$$, consisting of zeros and ones. You can perform the following operation exactly once:

1. Choose an integer $$$p$$$ ($$$1 \le p \le n$$$).
2. Reverse the substring $$$s_1 s_2 \ldots s_p$$$. After this step, the string $$$s_1 s_2 \ldots s_n$$$ will become $$$s_p s_{p-1} \ldots s_1 s_{p+1} s_{p+2} \ldots s_n$$$.
3. Then, perform a cyclic shift of the string $$$s$$$ to the left $$$p$$$ times. After this step, the initial string $$$s_1s_2 \ldots s_n$$$ will become $$$s_{p+1}s_{p+2} \ldots s_n s_p s_{p-1} \ldots s_1$$$.

For example, if you apply the operation to the string 110001100110 with $$$p=3$$$, after the second step, the string will become 011001100110, and after the third step, it will become 001100110011.

A string $$$s$$$ is called $$$k$$$-proper if two conditions are met:

- $$$s_1=s_2=\ldots=s_k$$$;
- $$$s_{i+k} \neq s_i$$$ for any $$$i$$$ ($$$1 \le i \le n - k$$$).

For example, with $$$k=3$$$, the strings 000, 111000111, and 111000 are $$$k$$$-proper, while the strings 000000, 001100, and 1110000 are not.

You are given an integer $$$k$$$, which is a divisor of $$$n$$$. Find an integer $$$p$$$ ($$$1 \le p \le n$$$) such that after performing the operation, the string $$$s$$$ becomes $$$k$$$-proper, or determine that it is impossible. Note that if the string is initially $$$k$$$-proper, you still need to apply exactly one operation to it.

## Input Format
Each test consists of multiple test cases. The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$1 \le k \le n$$$, $$$2 \le n \le 10^5$$$) — the length of the string $$$s$$$ and the value of $$$k$$$. It is guaranteed that $$$k$$$ is a divisor of $$$n$$$.

The second line of each test case contains a binary string $$$s$$$ of length $$$n$$$, consisting of the characters 0 and 1.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$.

## Output Format
For each test case, output a single integer — the value of $$$p$$$ to make the string $$$k$$$-proper, or $$$-1$$$ if it is impossible.

If there are multiple solutions, output any of them.

## Examples
```input
7
8 4
11100001
4 2
1110
12 3
111000100011
5 5
00000
6 1
101001
8 4
01110001
12 2
110001100110
```
```output
3
-1
7
5
4
-1
3
```

## Note
In the first test case, if you apply the operation with $$$p=3$$$, after the second step of the operation, the string becomes 11100001, and after the third step, it becomes 00001111. This string is $$$4$$$-proper.

In the second test case, it can be shown that there is no operation after which the string becomes $$$2$$$-proper.

In the third test case, if you apply the operation with $$$p=7$$$, after the second step of the operation, the string becomes 100011100011, and after the third step, it becomes 000111000111. This string is $$$3$$$-proper.

In the fourth test case, after the operation with any $$$p$$$, the string becomes $$$5$$$-proper.

Now solve the problem and return the code.