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

N,K=map(int,input().split())
o=[tuple(map(int,input().split())) for _ in range(N)]
ans=float("inf")

for i,j in combinations(o,2):
    x1,y1=i
    x2,y2=j
    xmax,xmin=max(x1,x2),min(x1,x2)

    for k,l in combinations(o,2):
        x3,y3=k
        x4,y4=l
        ymax,ymin=max(y3,y4),min(y3,y4)

        v=0
        for m in o:
            x5,y5=m
            if xmin<=x5<=xmax and ymin<=y5<=ymax:
                v+=1
        
        if v>=K:
            ans=min(ans,(ymax-ymin)*(xmax-xmin))


print(ans)