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:
from itertools import combinations as comb
n,k=map(int,input().split())
f=lambda x,y:(min(x,y),max(x,y))
o=[tuple(map(int,input().split())) for _ in range(n)]

v=float("inf")
for (a,b) in comb(range(n),2):
  for (c,d) in comb(range(n),2):
    lx,rx=f(o[a][0],o[b][0])
    dy,uy=f(o[c][1],o[d][1])
    cnt=0
    for i in o:
      if lx<=i[0]<=rx and dy<=i[1]<=uy:
        cnt+=1
    if cnt>=k:
      v=min(v,(rx-lx)*(uy-dy))
print(v)