N people are arranged in a row from left to right.

You are given a string S of length N consisting of 0 and 1, and a positive integer K.

The i-th person from the left is standing on feet if the i-th character of S is 0, and standing on hands if that character is 1.

You will give the following direction at most K times (possibly zero):

Direction: Choose integers l and $r satisfying 1 \leq l \leq r \leq N$, and flip the l-th, (l+1)-th, ..., and r-th persons. That is, for each i = l, l+1, ..., r, the i-th person from the left now stands on hands if he/she was standing on feet, and stands on feet if he/she was standing on hands.

Find the maximum possible number of consecutive people standing on hands after at most K directions.

Constraints

• N is an integer satisfying $1 \leq N \leq 10^5$.
• K is an integer satisfying $1 \leq K \leq 10^5$.
• The length of the string S is N.
• Each character of the string S is 0 or 1.

Input

Input is given from Standard Input in the following format:

N K
S

Output

Print the maximum possible number of consecutive people standing on hands after at most K directions.

Examples

Input

5 1
00010

Output

4

Input

14 2
11101010110011

Output

8

Input

1 1
1

Output

1

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