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 = [list(map(int,input().split())) for _ in range(n)]
x_y = sorted(x_y,key=lambda x:(x[0],x[1]))
ans = float('inf')
for i in range(n-1):
    for j in range(i+1,n):
        if j-i+1<k:
            continue
        dis_x = x_y[j][0]-x_y[i][0]
        y_x = x_y[i:j+1]
        y_x = sorted(y_x,key=lambda x:x[1])
        for l in range(len(y_x)-1):
            for m in range(l+1,len(y_x)):
                if m-l+1<k:
                    continue
                dis_y = y_x[m][1]-y_x[l][1]
                ans = min(ans,dis_x*dis_y)
print(ans)