Score: $425$ points

问题陈述

给定一个排列 $P = (P_1, P_2, \dots, P_N)$，它是 $(1, 2, \dots, N)$ 的一个排列。

如果一个长度为 $K$ 的索引序列 $(i_1, i_2, \dots, i_K)$ 满足以下两个条件，则称其为一个好索引序列：

• $1 \leq i_1 < i_2 < \dots < i_K \leq N$。
• 子序列 $(P_{i_1}, P_{i_2}, \dots, P_{i_K})$ 可以通过重新排列某些连续的 $K$ 个整数获得。 形式上，存在一个整数 $a$ 使得 $\lbrace P_{i_1},P_{i_2},\dots,P_{i_K} \rbrace = \lbrace a,a+1,\dots,a+K-1 \rbrace$。

在所有好索引序列中，找到 $i_K - i_1$ 的最小值。可以证明，在这个问题的约束条件下，至少存在一个好索引序列。

以上为大语言模型 kimi 翻译，仅供参考。

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.

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.

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.

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