Handstand

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

inputFormat

Input

Input is given from Standard Input in the following format:

N K S

outputFormat

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

样例

5 1
00010

4