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 (7.3.0) (judge verdict: Accepted)

import itertools
N, K = map(int, input().split())
xy = []
x, y = [], []
for i in range(N):
    a, b = map(int, input().split())
    xy.append([a, b])
    x.append(a)
    y.append(b)

ans = float('inf')
for sx, ex in itertools.combinations(x, 2):
    for sy, ey in itertools.combinations(y, 2):
        if ex < sx:
            sx, ex = ex, sx
        if ey < sy:
            sy, ey = ey, sy
        s = (ex-sx)*(ey-sy)
        if s == 0:
            continue

        c = 0
        for k in range(N):
            a, b = xy[k]
            if sx <= a and a <= ex and sy <= b and b <= ey:
                c += 1
        if c >= K and s < ans:
            ans = s

print(ans)