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: Wrong Answer)

N,K = gets.split.map &:to_i
Xs = (0...N).map{ |i| [i, *(gets.split.map &:to_i)] }.sort_by{ |i,x,y| x }
Ys = Xs.sort_by{ |i,x,y| y }
ans = 10**22
(0...N).each{ |i1|
  l = Xs[i1]
  set = (1 << i1)
  (i1+1...N).each{ |i2|
    r = Xs[i2]
    w = r[1] - l[1]
    set |= (1 << i2)
    (0...N).each{ |j1|
      d = Ys[j1]
      s2 = 0
      c2 = 0
      (j1...N).each{ |j2|
        u = Ys[j2]
        b2 = (1 << u[0])
        if (set & b2) != 0
          s2 |= b2
          c2 += 1
        end
        h = u[2] - d[2]
        if c2 >= K
          ans = [ans, w*h].min
        end
      }
    }
  }
}
p ans