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: Accepted)

# -*- coding: utf-8 -*-
from itertools import combinations

n,k = map(int, input().split())

xl = []
yl = []
xy = []
for _ in range(n):
    x,y = map(int, input().split())
    xl.append(x)
    yl.append(y)
    xy.append((x,y))
yl.sort()
xy.sort(key=lambda x:x[1])

res = None
for cx in combinations(xl, 2):
    x1,x2 = cx
    if x2>x1:
        x1,x2 = x2,x1

    for y2 in yl:
        cnt = 0
        for c in xy:
            x,y = c
            if x1>=x>=x2 and y>=y2:
                cnt += 1

            if cnt==k:
                y1 = y
                s = (x1-x2)*(y1-y2)
                if res is None:
                    res = s
                else:
                    res = min(res, s)
                break

print(res)