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 (2.3.3) (judge verdict: Time Limit Exceeded)

N,K=gets.split.map(&:to_i)
ls=N.times.map{gets.split.map(&:to_i)}
ans=Float::INFINITY
ls.combination(K>=4 ? 4 : K) do |a|
    b=a.transpose
    next if (K>=4 ? 4 : K) != b[0].uniq.size || (K>=4 ? 4 : K) != b[1].uniq.size
    ix,ax=b[0].minmax
    iy,ay=b[1].minmax
    cnt=0
    ls.each do |i|
        x,y=i[0],i[1]
        cnt+=1 if ix<=x && x<=ax && iy<=y && y<=ay
    end
    ans = ans > (ax-ix)*(ay-iy) ? (ax-ix)*(ay-iy) : ans if cnt>=K
end
puts ans