Given n sticks' lengths, determine whether there is a solution to choose 2k out of them and use these 2k sticks to form two k-convex polygons (non-degenerated), namely, two convex polygons each has exactly k sticks as its sides, and every adjacent sticks are not parallel.

Input
The first line contains two space-separated integers n and k, denoting the number of sticks and the size of convex polygon we needed.
The second line contains n positive integers, denoting the lengths of sticks.

Output
Print "Yes" (without quotes) in the first line if exists a solution. Otherwise print "No" (without quotes) instead.
If such solution exists, you should output a plan in the second line. Print 2k indexes (indexes start from 1) of the sticks you chosen. First k sticks compose the first k-convex polygon. And the later k sticks form the second. If there are more than one solution, output any.

Constraints

2k ≤ n ≤ 1000
3 ≤ k ≤ 10
1 ≤ length of each stick ≤ 10^9

Example

Input 1:
6 3
1 1 1 2 2 2

Output 1:
Yes
1 2 3 4 5 6

Input 2:
6 3
1 2 3 100 200 300

Output 2:
No

Explanation
Example case 1: 1 1 1 and 2 2 2 form two triangles.
Example case 2: Please be careful that convex polygons must be non-degenerated.

见题面

见题面