Problem Statement

You are given a string of length $N$, $S=S_1S_2\dots S_N$, consisting of 0, 1, and ?.

We like to replace every ? with 0 or 1 so that all of the following conditions are satisfied.

• $S$ contains exactly $K$ occurrences of 1.
• These $K$ occurrences of 1 are consecutive. That is, there is an $i\ (1 \leq i \le N-K+1)$ such that $S_i=S_{i+1}=\dots=S_{i+K-1}=$ 1.

Determine whether there is exactly one way to replace the characters to satisfy the conditions.

You have $T$ test cases to solve.

Constraints

• $1 \leq T \leq 10^5$
• $1 \leq K < N \leq 3 \times 10^5$
• $S$ is a string of length $N$ consisting of 0, 1, and ?.
• The sum of $N$ across the test cases is at most $3 \times 10^5$.

Input

The input is given from Standard Input in the following format:

T
\mathrm{case}_1
\vdots
\mathrm{case}_T

Each case is in the following format:

N K
S

Output

Print $T$ lines. The $i$-th line should contain Yes if, for the $i$-th test case, there is exactly one way to replace the characters to satisfy the conditions, and No otherwise.