Max MEX

AtCoder

IDabc290_c

Time2000ms

Memory256MB

Difficulty—

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 $X$. ## Constraints * All values in the input are integers. * $1 \le K \le N \le 3 \times 10^5$ * $0 \le A_i \le 10^9$ ## Input The input is given from Standard Input in the following format: $N$ $K$ $A_1$ $A_2$ $\dots$ $A_N$ [samples]

Samples

Input #1

7 3
2 0 2 3 2 1 9

Output #1

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 $3$.

API Response (JSON)

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