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 (2.7.6) (judge verdict: Time Limit Exceeded)

from sys import stdin
n,k = map(int,stdin.readline().split())
a = []
for i in xrange(n):
 a.append(map(int,stdin.readline().split()))
def solve(i,j,u,v):
 cnt = 0
 minx = min(a[i][0],a[j][0])
 maxx =  max(a[i][0],a[j][0])
 miny = min(a[i][1],a[j][1])
 maxy = max(a[i][1],a[j][1])
 
 minx1 = min(a[u][0],a[v][0])
 maxx1 =  max(a[u][0],a[v][0])
 miny1 = min(a[u][1],a[v][1])
 maxy1 = max(a[u][1],a[v][1])
 
 minx = min(minx,minx1)
 miny = min(miny,miny1)
 maxx = max(maxx,maxx1)
 maxy = max(maxy,maxy1)
 #print "solving",i,j,u,v,minx,maxx,miny,maxy
 for m in xrange(n):
  if a[m][0]>=minx and a[m][0]<=maxx and a[m][1]>=miny and a[m][1]<=maxy:
   cnt+=1
 #print "has",cnt
 if cnt>=k:
  return (maxx-minx)*(maxy-miny)
 return 10**100
ans = 10**50
for i in xrange(n):
 for j in xrange(n):
  for u in xrange(n):
   for v in xrange(n):
    ans = min(ans,solve(i,j,u,v))
print ans