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 = sorted([list(map(int,input().split())) for _ in range(N)],key = lambda x:(x[0],x[1]))

ans = 10**20

for i in range(K,N+1):
    for j in range(0,N-i+1):
        xy2 = sorted(xy[j:j+i],key = lambda x:(x[1]))
        for k in range(0,i-K+1):
            xy3 = xy2[k:k+K]
            Y_wid = xy3[-1][1] - xy3[0][1]
            x3 = [tmp for tmp,_ in xy3]
            X_wid = max(x3) - min(x3)
            ans = min(ans,X_wid*Y_wid)
print(ans)