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 (3.8.2) (judge verdict: Accepted)

def abc075_d():
    n, k = map(int, input().split())
    P = []
    xarr = []
    yarr = []
    for _ in range(n):
        x, y = (int(x) for x in input().split())
        P.append((x, y))
        xarr.append(x)
        yarr.append(y)
    xarr.sort()
    yarr.sort()

    ans = 5*10**18
    for s, xi in enumerate(xarr):
        for xj in xarr[s+1:]:
            cand = [(x, y) for x, y in P if xi <= x and x <= xj]
            for t, yi in enumerate(yarr):
                for yj in yarr[t+1:]:
                    cnt = len([y for x, y in cand if yi <= y and y <= yj])
                    if cnt >= k:
                        area = (xj - xi) * (yj - yi)
                        ans = min(ans, area)
    print(ans)

if __name__ == '__main__':
    abc075_d()