Problem Description

Rasuk has a sequence of length $N$, denoted as $a$.

The boringness of a sequence is defined as the maximum length of a contiguous subsequence where all elements are the same.

Rasuk wants to change up to $K$ elements of the sequence $a$ to any integer in order to minimize the boringness.

Find the minimum boringness that can be achieved.

Input Format

The input is given from the standard input in the following format:

$ N $ $ K $ $ a_1 $ $ a_2 $ $\ldots$ $ a_N $

Output Format

Output the minimum boringness when up to $K$ elements of the sequence $a$ are changed.

Sample Input and Output

Sample Input #1

10 2
3 3 3 3 4 4 4 4 4 4

Sample Output #1

3

Sample Input #2

9 2
3 3 4 4 4 4 4 4 4

Sample Output #2

2

Sample Input #3

5 5
3 1 4 1 5

Sample Output #3

1

Notes/Hints

Constraints

• All input values are integers.
• $1 \leq K \leq N \leq 2 \times 10^5$
• $1 \leq a_i \leq N$

Sample Explanation 1

Changing the 1st element to $1$ and the 7th element to $2$, the sequence becomes $1, 3, 3, 3, 4, 4, 2, 4, 4, 4$, and the boringness is $3$.

Sample Explanation 2

Changing the 4th element to $5$ and the 7th element to $1$, the sequence becomes $3, 3, 4, 5, 4, 4, 1, 4, 4$, and the boringness is $2$.

Sample Explanation 3

No changes are necessary.

见题面 Input 部分

见题面 Output 部分