### Problem Statement

You are given a length-$N$ sequence of non-negative integers.  
When $B$ is a sequence obtained by choosing $K$ elements from $A$ and concatenating them without changing the order, find the maximum possible value of $MEX(B)$.

Here, for a sequence $X$, we define $MEX(X)$ as the unique non-negative integer $m$ that satisfies the following conditions:

-   Every integer $i$ such that $0 \le i < m$ is contained in $X$.
-   $m$ is not contained in $X$.

### Input

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

```
$N$ $K$
$A_1$ $A_2$ $\dots$ $A_N$
```

### Output

Print the answer.

### Constraints

-   All values in the input are integers.
-   $1 \le K \le N \le 3 \times 10^5$
-   $0 \le A_i \le 10^9$

3

In this input, A=(2,0,2,3,2,1,9), and you obtain the sequence B by picking K=3 elements. For example,

• If the 1-st, 2-nd, and 3-rd elements are chosen, MEX(B)=MEX(2,0,2)=1.
• If the 3-rd, 4-th, and 6-th elements are chosen, MEX(B)=MEX(2,3,1)=0.
• If the 2-nd, 6-th, and 7-th elements are chosen, MEX(B)=MEX(0,1,9)=2.
• If the 2-nd, 3-rd, and 6-th elements are chosen, MEX(B)=MEX(0,2,1)=3.

The maximum possible MEX is 3.