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 (2.7.6) (judge verdict: Accepted)

n, k = map(int, raw_input().split())
p = [map(int, raw_input().split()) for i in range(n)]
p = sorted(p, key=lambda _: _[0])
ans = 10**30
for b in range(n):
    x_b, y_b = p[b]
    for t in range(n):
        x_t, y_t = p[t]
        if y_t <= y_b:
            continue
        v = filter(lambda _: y_b <= _[1] <= y_t, p)
        for i in range(len(v) - k + 1):
            x_i, y_i = v[i]
            x_j, y_j = v[i+k-1]
            ans = min(ans, (x_j - x_i) * (y_t - y_b))
print ans