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)

def solve(N, K, XYs):
    ans = 10 ** 19 + 1
    Ys = [y for x, y in XYs]
    Xs = [x for x, y in XYs]
    for y1 in Ys:
        for y2 in Ys:
            if y1 >= y2:
                continue
            for x1 in Xs:
                for x2 in Xs:
                    if x1 >= x2:
                        continue
                    y1, y2 = min(y1, y2), max(y1, y2)
                    x1, x2 = min(x1, x2), max(x1, x2)
                    if len([(x, y) for x, y in XYs if x1 <= x <= x2 and y1 <= y <= y2]) >= K:
                        ans = min(ans, abs(y2 - y1) * abs(x2 - x1))
    return ans

if __name__ == "__main__":
    N, K = tuple(map(int, input().split(" ")))
    XYs = [tuple(map(int, input().split(" "))) for _ in range(N)]
    print(solve(N, K, XYs))