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:
# coding: utf-8
# Here your code !
n,k=[int(x) for x in input().split()]
x=[0]*n
y=[0]*n
for i in range(n):
   x[i],y[i]=[int(x) for x in input().split()]
from itertools import product
ans=float("inf")
for xmax,xmin,ymax,ymin in product(x,x,y,y):
    if xmax<=xmin or ymax<=ymin or (xmax-xmin)*(ymax-ymin)>=ans:
        continue
    if len([0 for xi,yi in zip(x,y) if xmin<=xi<=xmax and ymin<=yi<=ymax])>=k:
        ans=(xmax-xmin)*(ymax-ymin)
print(ans)