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: Wrong Answer)

n, k = [int(_) for _ in input().split()]
x, y = [], []
for _ in range(n):
    temp = [int(_) for _ in input().split()]
    x.append(temp[0])
    y.append(temp[1])
x.sort()
y.sort()

answer = 4 * 10**18
for i0 in range(n):
    for j0 in range(i0 + 1, n):
        xi = x[i0]
        xj = x[j0]
        for i1 in range(n):
            for j1 in range(i1 + 1, n):
                yi = y[i1]
                yj = y[j1]
                c = 0
                for l in range(n):
                    if xi <= x[l] and x[l] <= xj and yi <= y[l] and y[l] <= yj:
                        c += 1
                s = (xj - xi) * (yj - yi)
                if s <= answer and c >= k:
                    answer = s

print(answer)