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 (3.4.3) (judge verdict: Time Limit Exceeded)

n, k = map(int, input().split())
xy = []
for i in range(n):
    xy.append(list(map(int, input().split())))
s = []
x = [xy[i][0] for i in range(n)]
y = [xy[i][1] for i in range(n)]
x.sort()
y.sort()
for i in range(n):
    for j in range(n):
        for l in range(i + 1, n):
            x1 = x[i]
            y1 = y[j]
            x2 = x[l]
            y2 = j - 1
            count = 0
            while count < k:
                y2 += 1
                if y2 >= n:
                    break
                for m in range(n):
                    if y[y2] == y1:
                        if x1 <= xy[m][0] <= x2 and xy[m][1] == y1:
                            count += 1
                    elif x1 <= xy[m][0] <= x2 and y[y2 - 1] < xy[m][1] <= y[y2]:
                        count += 1
            else:
                s.append((x2 - x1) * (y[y2] - y1))
print(min(s))