Vlad found a binary string$$$^{\text{∗}}$$$ $$$s$$$ of even length $$$n$$$. He considers a pair of indices ($$$i, n - i + 1$$$), where $$$1 \le i \lt n - i + 1$$$, to be good if $$$s_i = s_{n - i + 1}$$$ holds true.

For example, in the string '010001' there is only $$$1$$$ good pair, since $$$s_1 \ne s_6$$$, $$$s_2 \ne s_5$$$, and $$$s_3=s_4$$$. In the string '0101' there are no good pairs.

Vlad loves palindromes, but not too much, so he wants to rearrange some characters of the string so that there are exactly $$$k$$$ good pairs of indices.

Determine whether it is possible to rearrange the characters in the given string so that there are exactly $$$k$$$ good pairs of indices ($$$i, n - i + 1$$$).

$$$^{\text{∗}}$$$A string $$$s$$$ is called binary if it consists only of the characters '0' and '1'

Input

The first line contains an integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

The first line of each test case contains two integers $$$n$$$ and $$$k$$$ ($$$2 \le n \le 2 \cdot 10^5$$$, $$$0 \le k \le \frac{n}{2}$$$, $$$n$$$ is even) — the length of the string and the required number of good pairs.

The second line of each test case contains a binary string $$$s$$$ of length $$$n$$$.

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

Output

For each test case, output "YES" if there is a way to rearrange the characters of the string so that there are exactly $$$k$$$ good pairs, otherwise output "NO".

You may output each letter in any case (lowercase or uppercase). For example, the strings "yEs", "yes", "Yes", and "YES" will be accepted as a positive answer.

Not Quite a Palindromic String

Examples