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 = [0]*n
Y = [0]*n
for i in range(n):
    X[i],Y[i] = map(int,input().split())

Xs = sorted(X)
Ys = sorted(Y)
XY = sorted(list(zip(X,Y)))
ans = 1e100
for i in range(n-k+1):
    for j in range(i+k-1,n):
        w = Xs[j] - Xs[i]
        XYs = sorted(XY[i:j+1],key = lambda x:x[1])
        h = 1e100
        for l in range(len(XYs) - k + 1):
            h = min(h, XYs[l + k - 1][1] - XYs[l][1])
        ans = min(ans , h*w)
print(ans)