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 Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import Control.Monad

main :: IO ()
main = do
    [n, k] <- map read . words <$> getLine :: IO [Integer]
    pos <- replicateM (fromIntegral n) ((\[a,b]->(a,b)) . map read . words <$> getLine) :: IO [(Integer, Integer)]
    print . minimum $ flip concatMap
        [((x,y), (x',y'))|x<-map fst pos,x<-map fst pos, x'<-map fst pos, y<-map snd pos, y'<- map snd pos] 
        (\(p,p')-> if innerPoints pos p p' >= k then [(fst p'-fst p)*(snd p'-snd p)] else []) 
    
innerPoints :: [(Integer, Integer)] -> (Integer, Integer) -> (Integer, Integer) -> Integer
innerPoints pos (x,y) (x',y') = sum . map (\x->if x then 1 else 0) $ flip map pos
    (\(x'',y'')->x<=x'' && x''<=x' && y<=y'' && y''<=y')