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)

import itertools
n,k=map(int,input().split())
X,Y,XY=[],[],[]
for i in range(n):
  x,y=map(int,input().split())
  X.append(x)
  Y.append(y)
  XY.append([x,y])
def count(x1,x2,y1,y2):
  ct=0
  if x1>x2:
    x1,x2=x2,x1
  if y1>y2:
    y1,y2=y2,y1
  for x,y in XY:
    if x1<=x<=x2 and y1<=y<=y2:
      ct+=1
  return ct
ans=float("inf")
for x1,x2 in itertools.combinations(X,2):
  for y1,y2 in itertools.combinations(Y,2):
    if count(x1,x2,y1,y2)==k:
      ans=min(ans,abs((x1-x2)*(y1-y2)))
print(ans)