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: Accepted)

n, k = map(int, input().split())
XY = []
xs = []
ys = []
for i in range(n):
    x, y = map(int, input().split())
    XY.append((x, y))
    xs.append(x)
    ys.append(y)

xs.sort()
ys.sort()
ans = float('inf')
for a in range(n-1):
    for b in range(a+1, n):
        for c in range(n-1):
            for d in range(c+1, n):
                xl = xs[a]
                xr = xs[b]
                yl = ys[c]
                yu = ys[d]
                cnt = 0
                for x, y in XY:
                    if xl <= x <= xr and yl <= y <= yu:
                        cnt += 1
                if cnt >= k:
                    ans = min(ans, (xr-xl)*(yu-yl))
print(ans)