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())
x=[]
y=[]
xy=[]
for _ in range(n):
  xx,yy=map(int,input().split())
  xy.append((xx,yy))
  x.append(xx)
  y.append(yy)
xx=sorted(x)
yy=sorted(y)
ans=10**20
for sxi in range(n-1):
  for syi in range(n-1):
    for tyi in range(1,n):
      sx,sy,ty=xx[sxi],yy[syi],yy[tyi]
      ax=sorted([xxx for xxx,yyy in xy if sx<=xxx and sy<=yyy<=ty])
      if len(ax)<k:continue
      tx=ax[k-1]
      ans=min(ans,(tx-sx)*(ty-sy))
print(ans)