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 Python (3.4.3) (judge verdict: Accepted)

N,K = map(int,input().split())
point = []
y_list = []

for _ in range(N):
    x,y = map(int, input().split())
    point.append((x,y))
    y_list.append(y)
point = sorted(point,key=lambda tup: tup[0])
y_list.sort()
min_area = (y_list[N-1] - y_list[0]) * (point[N-1][0] - point[0][0])

for by in range(N):
    for ty in range(by+1,N):
        size=0
        idx = [0 for _ in range(N)]
        for i in range(N):
            if (y_list[by] <= point[i][1] and y_list[ty] >= point[i][1]):
                idx[size] = i
                size +=1
        lb = 0
        while(lb + K -1 < size):
            min_area = min(min_area, (y_list[ty] - y_list[by]) * (point[idx[lb + K - 1]][0] - point[idx[lb]][0]))
            lb+=1
print(min_area)