You are given a permutation $a$ of length $n$. You are also given positive integers $k$ and $m$ ($1 \le k \le m \le n$).

You are asked to tell whether there exists a subsequence $b$ of $a$ of length $m$ such that the length of the longest increasing subsequence of $b$ equals $k$. In case such a subsequence exists, you are asked to print any correct one.

Input

First line contains three integers $n, m, k$ ($1 \le k \le m \le n \le 5\,000$) — length of the permutation, length of the subsequence $b$, and length of the longest increasing subsequence of $b$.

Output

In the first line, output “Yes” or “No”. Checker is case insensitive.

In the second line, output one of the correct subsequences if such exists.

Examples

Input 1

5 2 2
4 5 3 2 1

Output 1

Yes
4 5

Input 2

5 2 2
5 4 3 2 1

Output 2

No

Input 3

6 4 2
1 3 4 2 6 5

Output 3

Yes
4 2 6 5