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.

The input is given from Standard Input in the following format:

```
$N$ $K$
$P_1$ $P_2$ $\dots$ $P_N$
```

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

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

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 $1≤i_1<i_2≤N$ 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.

0

$i_K−i_1=i_1−i_1=0$ in all good index sequences.