Giải bài trực tuyến

Given a convex polygon of N vertices. The vertices are numbered from 1 to N. Your task is to pick K vertices among these N vertices so that they form a polygon having the maximum possible area.

Input

• The first line contains two integers N and K (3 ≤ K ≤ N ≤ 200).
• The u^th line in the next N lines contains two integers X_u and Y_u which are the coordinates of the u^th vertex. The vertices are given in clockwise order. The absolute values of all the coordinates do not exceed 10⁵.

Output

• The first line should contain the maximum area of a K-vertices polygon (rounding up to 2 decimal places).
• The second line contains an increasing sequence of K numbers which are the indexes of the chosen vertices.

Example

Input
4 3
1 2
3 1
2 0
1 1

Output
1.50
1 2 3