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)

def main():
    N, K = map(int, input().split())
    XY = (tuple(map(int, input().split())) for _ in [0] * N)

    x = [0] * N
    y = [0] * N
    for i, (j, k) in enumerate(XY):
        x[i] = j
        y[i] = k

    ans = float('inf')
    for xi in range(N):
        for xj in range(N):
            for yi in range(N):
                for yj in range(N):
                    cnt = 0
                    for i in range(N):
                        if x[xi] <= x[i] <= x[xj] and y[yi] <= y[i] <= y[yj]:
                            cnt += 1
                    if cnt >= K:
                        ans = min(ans, (x[xj] - x[xi]) * (y[yj] - y[yi]))

    print(ans)

main()