P9644 [SNCPC2019] Turn It Off

It's already 21:30 now, and it's time for BaoBao to go to bed. To ensure his sleeping quality, BaoBao decides to turn all the lights in his bedroom off. There are $n$ lights, numbered from 1 to $n$, arranged in a row in BaoBao's bedroom. Each time BaoBao can select an integer $i$ and turn all the lights numbered from $i$ to $(i+L-1)$ (both inclusive) off, where $L$ is a predefined positive integer. Note that each time the value of $L$ must be the same. Given the initial status of all the lights, please help BaoBao determine the smallest possible $L$ so that he can turn all the lights off within $k$ times.

There are multiple test cases. The first line of the input contains an integer $T$, indicating the number of test cases. For each test case: The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 2 \times 10^5$). The second line contains a string $s$ ($|s| = n$, $s \in \{\text{`0'}, \text{`1'}\}$) indicating the initial status of the lights. Let $s_i$ be the $i$-th character in $s$, if $s_i = \text{`1'}$ then the $i$-th light is initially on, otherwise it's initially off. It's guaranteed that there is at least one `1· in $s$. It's guaranteed that the sum of $n$ of all test cases will not exceed $2 \times 10^6$.

For each test case output one line containing one integer, indicating the smallest possible $L$.