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.

Samples

6
6 2
000000
2 1
01
4 1
1011
10 2
1101011001
10 1
1101011001
2 1
11

NO
NO
YES
NO
YES
YES