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 = map(int, input().split())
    p = []
    for _ in range(N):
        x, y = map(int, input().split())
        p.append([x, y])
    p.sort(key = lambda x: x[0])

    min_area = float('inf')
    for i in range(N-1):
        for j in range(i+1, N):
            if j-i+1 >= K:
                x1 = p[i][0]
                x2 = p[j][0]
                ys = []
                for k in range(i, j+1):
                    ys.append(p[k][1])
                ys.sort()
                for k in range(len(ys)):
                    for l in range(k+K-1, len(ys)):
                        y1 = ys[k]
                        y2 = ys[l]
                        area = (x2-x1)*(y2-y1)
                        if area > 0:
                            min_area = min(min_area, area)
    return min_area