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 Lua (5.3.2) (judge verdict: Time Limit Exceeded)

n, k = io.read('n'), io.read('n')
x, y = {}, {}
for i = 1, n do x[i], y[i] = io.read('n'), io.read('n') end

ans = 1 << 62

for l = 1, n do
    for r = 1, n do if x[r] > x[l] then
        for u = 1, n do
            for d = 1, n do if y[u] > y[d] then
                local count = 0
                for i = 1, n do
                    if x[i] >= x[l] and x[i] <= x[r] and
                        y[i] >= y[d] and y[i] <= y[u]
                    then
                        count = count + 1
                    end
                end
                if count >= k then
                    ans = math.min(ans, (x[r] - x[l]) * (y[u] - y[d]))
                end
            end end
        end
    end end
end

print(ans)