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: Runtime Error)

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 <$> getLine) :: IO [(Integer, Integer)]
    ns <- concat <$> mapM (innerPoints pos k) [(p, p',p'')| p<-pos, p'<-pos, p''<-pos]
    print . minimum $ ns

innerPoints :: [(Integer, Integer)] 
            -> Integer
            -> ((Integer,Integer), (Integer,Integer), (Integer,Integer))
            -> IO [Integer]
innerPoints pos k ((x,y), (x', y'),(x'', y'')) = let
    isInner (x''', y''') =  minimum [x,x',x''] <= x''' && x''' <= maximum [x,x',x'']
                         && minimum [y,y',y''] <= y''' && y''' <= maximum [y,y',y'']
    innerP = sum . map (\b->if b then 1 else 0) $ map isInner pos
    in return [(maximum [x,x',x'']-minimum [x,x',x'']) * (maximum [y,y',y''] - minimum [y,y',y'']) | innerP >= k]