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)

import sys
N,K=map(int,sys.stdin.readline().split())
A=sorted([int(e) for e in sys.stdin.readline().split()] for _ in range(N))
x,y=zip(*A)
Y=sorted(y)
r=(x[-1]-x[0])*(Y[-1]-Y[0])
for i in range(N):
 for j in range(i+1,N):
  for k in range(N):
   for l in range(k+1,N):
    ly=Y[k];ry=Y[l];q=(x[j]-x[i])*(ry-ly)
    if r>q and K<=(j-i+1) and K<=sum(ly<=y[z]<=ry for z in range(i,j+1)): r=q
print(r)