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: Time Limit Exceeded)

import itertools

n , k = map(int, input().split())
points = [list(map(int, input().split())) for i in range(n)]
sorted_x_list = sorted([point[0] for point in points])
sorted_y_list = sorted([point[1] for point in points])

area = float("inf")
for i, x_left in enumerate(sorted_x_list):
    for j, y_lower in enumerate(sorted_y_list):
        for x_right in sorted_x_list[i+1:]:
            for y_upper in sorted_y_list[j+1:]:
                count = 0
                for point in points:
                    if (x_left <= point[0] <= x_right
                        and y_lower <= point[1] <= y_upper):
                        count += 1
                if count >= k:
                    area = min(area, (x_right-x_left)*(y_upper-y_lower))
print(area)