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: Accepted)

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

-- Discretize
rx, ry = {}, {}
for i = 1, n do rx[i], ry[i] = {x[i], i}, {y[i], i} end
pair_cmp = function (lhs, rhs) return lhs[1] < rhs[1] end
table.sort(rx, pair_cmp)
table.sort(ry, pair_cmp)
for i = 1, n do x[rx[i][2]], y[ry[i][2]] = i, i end
for i = 1, n do rx[i], ry[i] = rx[i][1], ry[i][1] end

-- O(n^4)
-- Prefix sum
p = {}
for i = 0, n do
    p[i] = {}
    for j = 0, n do p[i][j] = 0 end
end
for i = 1, n do p[x[i]][y[i]] = 1 end
for i = 1, n do
    for j = 1, n do
        p[i][j] = p[i][j] + p[i - 1][j] + p[i][j - 1] - p[i - 1][j - 1]
    end
end

-- Iteration
ans = 1 << 62
for l = 1, n do
    for r = l + 1, n do
        for d = 1, n do
            for u = d + 1, n do
                if p[r][u] - p[l - 1][u] - p[r][d - 1] + p[l - 1][d - 1] >= k then
                    ans = math.min(ans, (rx[r] - rx[l]) * (ry[u] - ry[d]))
                end
            end
        end
    end
end

print(ans)