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())
li = [list(map(int, input().split())) for i in range(N)]
xx = [p[0] for p in li]
yy = [p[1] for p in li]
xx.sort()
yy.sort()
Min = (xx[N-1]-xx[0])*(yy[N-1]-yy[0])
for xi in range(N-1):
    for xj in range(xi+1, N):
        for yi in range(N-1):
            for yj in range(yi+1, N):
                cnt = 0
                for p in li:
                    [x, y] = p
                    if xx[xi] <= x <= xx[xj] and yy[yi] <= y <= yy[yj]:
                        cnt += 1
                if cnt >= K:
                    Min = min(Min, (xx[xj]-xx[xi])*(yy[yj]-yy[yi]))
print(Min)