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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

from itertools import product as pd
g=lambda x,y:(min(x,y),max(x,y))
n,k=map(int,input().split())
o=[tuple(map(int,input().split())) for _ in range(n)]

def f(a,b,c,d):
  lx,rx=g(o[a][0],o[b][0])
  dy,uy=g(o[c][1],o[d][1])
  cnt=0
  for i in o:
    if lx<=i[0]<=rx and dy<=i[1]<=uy:
      cnt+=1
  if cnt>=k:
    return (rx-lx)*(uy-dy)
  return float("inf")

v=float("inf")
for (a,c) in pd(range(n),repeat=2):
  for (b,d) in pd(range(n),repeat=2):
    v=min(v,f(a,b,c,d))
print(v)