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

\(1 \leq n \leq 10^6 \\ 1 \leq k \leq n\)