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())
XY=[list(map(int,input().split())) for i in range(N)]
l=[i for i in range(N)]
ans=float("inf")
for v in itertools.combinations(l,2):
  xmax=max(XY[v[0]][0],XY[v[1]][0])
  xmin=min(XY[v[0]][0],XY[v[1]][0])
  ymax=max(XY[v[0]][1],XY[v[1]][1])
  ymin=min(XY[v[0]][1],XY[v[1]][1])
  k=0
  for xy in XY:
    x,y=xy[0],xy[1]
    if xmin<=x and x<=xmax:
      if ymin<=y and y<=ymax:
        k+=1    
  if k>=K:
    ans=min(ans,(xmax-xmin)*(ymax-ymin))
    
for v in itertools.combinations(l,3):
  xmax=max(XY[v[0]][0],XY[v[1]][0],XY[v[2]][0])
  xmin=min(XY[v[0]][0],XY[v[1]][0],XY[v[2]][0])
  ymax=max(XY[v[0]][1],XY[v[1]][1],XY[v[2]][1])
  ymin=min(XY[v[0]][1],XY[v[1]][1],XY[v[2]][1])
  k=0
  for xy in XY:
    x,y=xy[0],xy[1]
    if xmin<=x and x<=xmax:
      if ymin<=y and y<=ymax:
        k+=1    
  if k>=K:
    ans=min(ans,(xmax-xmin)*(ymax-ymin))
    
for v in itertools.combinations(l,4):
  xmax=max(XY[v[0]][0],XY[v[1]][0],XY[v[2]][0],XY[v[3]][0])
  xmin=min(XY[v[0]][0],XY[v[1]][0],XY[v[2]][0],XY[v[3]][0])
  ymax=max(XY[v[0]][1],XY[v[1]][1],XY[v[2]][1],XY[v[3]][1])
  ymin=min(XY[v[0]][1],XY[v[1]][1],XY[v[2]][1],XY[v[3]][1])
  k=0
  for xy in XY:
    x,y=xy[0],xy[1]
    if xmin<=x and x<=xmax:
      if ymin<=y and y<=ymax:
        k+=1    
  if k>=K:
    ans=min(ans,(xmax-xmin)*(ymax-ymin))
print(ans)