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())
xy=[]
for i in range(n):
    tmp=[int(j) for j in input().split()]
    xy.append((tmp[0],tmp[1]))
from operator import itemgetter
xy.sort(key=itemgetter(1))
xy.sort(key=itemgetter(0))
xy=tuple(xy)
l=tuple(enumerate(xy))
ans=10**100
for i,(a,b) in l[:n-k+1]:
    for j,(c,d) in l[i+k-1:]:
        l1=sorted(y for x,y in xy[i:j+1])
        l2=l1[k-1:]
        for p,q in zip(l1,l2):
            if p<=b and q>=d:
                ans=min(ans,(c-a)*(q-p))
print(ans)