Problem Statement

You are given $a permutation P = (P_1, P_2, \dots, P_N)$ of $(1, 2, \dots, N)$.
A length-K sequence of indices $(i_1, i_2, \dots, i_K)$ is called a good index sequence if it satisfies both of the following conditions:

• $1 \leq i_1 < i_2 < \dots < i_K \leq N$.
• The subsequence $(P_{i_1}, P_{i_2}, \dots, P_{i_K})$ can be obtained by rearranging some consecutive K integers.
  Formally, there exists an integer a such that $\lbrace P_{i_1},P_{i_2},\dots,P_{i_K} \rbrace = \lbrace a,a+1,\dots,a+K-1 \rbrace$.

Find the minimum value of i_K - i_1 among all good index sequences. It can be shown that at least one good index sequence exists under the constraints of this problem.

Input

The input is given from Standard Input in the following format:
N K
$P_1 P_2 \dots P_N$

Output

Print the minimum value of i_K - i_1 among all good index sequences.

Constraints

• $1 \leq K \leq N \leq 2 \times 10^5$
• $1 \leq P_i \leq N$
• $P_i \neq P_j$ if $i \neq j$.
• All input values are integers.

Sample Input 1

4 2
2 3 1 4

Sample Output 1

1

The good index sequences are (1,2),(1,3),(2,4). For example, (i_1, i_2) = (1,3) is $a good index sequence because 1 \leq i_1 < i_2 \leq N$ and (P_{i_1}, P_{i_2}) = (2,1) is a rearrangement of two consecutive integers 1, 2.
Among these good index sequences, the smallest value of i_K - i_1 is for (1,2), which is 2-1=1.

Sample Input 2

4 1
2 3 1 4

Sample Output 2

0

i_K - i_1 = i_1 - i_1 = 0 in all good index sequences.

Sample Input 3

10 5
10 1 6 8 7 2 5 9 3 4

Sample Output 3

5

见题面 Input 部分

见题面 Output 部分