{"raw_statement":[{"iden":"statement","content":"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.\n\nThere 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.\n\nGiven 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."},{"iden":"input","content":"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:\n\nThe first line contains two integers $n$ and $k$ ($1 \\le k \\le n \\le 2 \\times 10^5$).\n\nThe 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 $s$.\n\nIt's guaranteed that the sum of $n$ of all test cases will not exceed $2 \\times 10^6$."},{"iden":"output","content":"For each test case output one line containing one integer, indicating the smallest possible $L$."}],"translated_statement":null,"sample_group":[["2\n10 4\n0101011111\n3 1\n010","3\n1"]],"show_order":[],"formal_statement":null,"simple_statement":null,"has_page_source":false}