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)

# -*- coding: utf-8 -*-

import sys
import itertools


def main():
    n, k = [int(x) for x in sys.stdin.readline().rstrip().split(" ")]

    data = []
    for line in sys.stdin:
        x, y = [int(i) for i in line.rstrip().split(" ")]
        data.append((x, y))

    s_min = float("inf")
    for d in itertools.combinations(data, k):
        x_max = max(d, key=lambda x: x[0])[0]
        x_min = min(d, key=lambda x: x[0])[0]
        y_max = max(d, key=lambda x: x[1])[1]
        y_min = min(d, key=lambda x: x[1])[1]

        s = (x_max - x_min) * (y_max - y_min)
        s_min = min(s, s_min)

    print(s_min)


if __name__ == "__main__":
    main()