There are $n$ bulbs arranged in a row. The state of the bulbs is represented by a binary string bulbs of length $n$, the $0$ at $i^{th}$ position in the string represents the bulb is OFF and $1$ represents the bulb is ON, where $0 \leq i < n$. You have to switch OFF all the bulbs by performing following operation atmost $k$ times. The operation is defined as:-

• Choose any index $i$ in the string bulb and turn OFF all the lights having indexes $i$ to $\min(n - 1, i + l - 1)$ (inclusive), where $l$ is a pre defined number, greater than zero and fixed for all the operations.

The task is to find the smallest value of $l$ greater than zero, such that you can turn OFF all the bulbs in atmost $k$ operations.

Input format

• The first line of input contains two space separated integers, $n$ and $k$, representing the size of string bulb and maximum number of operations you can perform.
• The second line of input contains a binary string, bulbs.

Output format

The output contains a single integer, the minimum possible value of $l$ greater than zero such that you are able to turn OFF all the bulbs in atmost $k$ operations.

Constraints

$1 \leq n \leq 10^6 \\ 1 \leq k \leq n$