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())
point=[]
for i in range(n):
    x,y=map(int,input().split())
    point.append((x,y))
point.sort()
ans=10**20
for i in range(n):
    for j in range(i+1,n):
        y_list=[]
        for p in range(i,j+1):
            y_list.append(point[p][1])
        y_list.sort()
        yl=len(y_list)
        y_d=10**10
        if yl<k:
            continue
        else:
            for p in range(yl-k+1):
                y_d=min(y_d,y_list[p+k-1]-y_list[p])
        x_d=point[j][0]-point[i][0]
        temp=x_d*y_d
        ans=min(ans,temp)
print(ans)