Problem:
Score : 400 points

Problem Statement

We have N points in a two-dimensional plane.

The coordinates of the i-th point (1 \leq i \leq N) are (x_i,y_i).

Let us consider a rectangle whose sides are parallel to the coordinate axes that contains K or more of the N points in its interior.

Here, points on the sides of the rectangle are considered to be in the interior.

Find the minimum possible area of such a rectangle.

Constraints

2 \leq K \leq N \leq 50

-10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)

x_i≠x_j (1 \leq i<j \leq N)

y_i≠y_j (1 \leq i<j \leq N)

All input values are integers. (Added at 21:50 JST)

Input

Input is given from Standard Input in the following format:

N K
x_1 y_1
:
x_{N} y_{N}

Output

Print the minimum possible area of a rectangle that satisfies the condition.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).

Its area is (8-1) × (4-1) = 21.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in Ruby (2.7.1) (judge verdict: Accepted)

N,K=gets.split.map(&:to_i)
v=[]
N.times{
    x,y=gets.split.map(&:to_i)
    v<<[x,y]
}
v.sort_by!{|o|o[0]}
s=10**20
(0 .. N-K).each{|l|
    (l+K-1 .. N-1).each{|r|
        w=v[r][0]-v[l][0]
        sy=v[l .. r].map{|o|o[1]}.sort
        (sy.size-K+1).times{|i|
            h=sy[i+K-1]-sy[i]
            warn [h,w*h].inspect
            if w*h<s
                s=w*h
            end
        }
    }
}
puts s