Problem: 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.

Examples

Input

4 4
1 4
3 3
6 2
8 1


Output

21


Input

4 2
0 0
1 1
2 2
3 3


Output

1


Input

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999


Output

3999999996000000001

Solution (in PYTHON3):

Solution:
N,K=map(int,input().split())
nodes=[]
for i in range(N):
  x,y=map(int,input().split())
  nodes.append((x,y))
nodes.sort()
import math
ans=math.inf
count=0
for i in range(N):
  for j in range(i+1,N):
    for k in range(N):
      for l in range(i+1,N):
        count=0
        for m in range(N):
          small=min(nodes[k][1],nodes[l][1])
          big=max(nodes[k][1],nodes[l][1])
          if nodes[i][0]<=nodes[m][0]<=nodes[j][0] and small<=nodes[m][1]<=big:
            count+=1
        if count>=K:
          ans=min(ans,(nodes[j][0]-nodes[i][0])*(big-small))
print(ans)