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.chomp.split(' ').map{|n| n.to_i}
XY = Array.new(N+1)
0.upto(N-1){|d|
	XY[d]=gets.chomp.split(' ').map{|n| n.to_i}
}
INT_MAX = 9999999999999999999999
min = INT_MAX
0.upto(N-1){|xsi|
	xs = XY[xsi][0]
	0.upto(N-1){|xei|
		xe = XY[xei][0]
		0.upto(N-1){|ysi|
			ys = XY[ysi][1]
			0.upto(N-1){|yei|
				ye = XY[yei][1]
				cnt = 0
				0.upto(N-1){|tgt|
					if(xs <= XY[tgt][0] && XY[tgt][0] <= xe && ys <=XY[tgt][1] && XY[tgt][1] <= ye)
						cnt += 1
					end
				}
				if(cnt >= K)
					area = (xe-xs) * (ye-ys)
					if(min > area)
						min = area
					end
				end
			}
		}
	}
}
puts min