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 PyPy3 (2.4.0) (judge verdict: Wrong Answer)

def main():
    N, K = (int(i) for i in input().split())
    xy = [[int(i) for i in input().split()] for _ in range(N)]

    ans = ((10**9)*2)**2 + 5
    xy.sort(key=lambda p: p[0])
    for i in range(N-K+1):
        x_min = (10**9)*2 + 5
        x_max = -((10**9)*2 + 5)
        y_min = (10**9)*2 + 5
        y_max = -((10**9)*2 + 5)
        for j in range(i, i+K):
            x_min = min(x_min, xy[j][0])
            x_max = max(x_max, xy[j][0])
            y_min = min(y_min, xy[j][1])
            y_max = max(y_max, xy[j][1])
        ans = min(ans, (x_max-x_min)*(y_max-y_min))
    xy.sort(key=lambda p: p[1])
    for i in range(N-K+1):
        x_min = (10**9)*2 + 5
        x_max = -((10**9)*2 + 5)
        y_min = (10**9)*2 + 5
        y_max = -((10**9)*2 + 5)
        for j in range(i, i+K):
            x_min = min(x_min, xy[j][0])
            x_max = max(x_max, xy[j][0])
            y_min = min(y_min, xy[j][1])
            y_max = max(y_max, xy[j][1])
        ans = min(ans, (x_max-x_min)*(y_max-y_min))
    print(ans)


if __name__ == '__main__':
    main()