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:
from itertools import combinations
def main():
    N, K = map(int, input().split())
    P = [list(map(int, input().split())) for _ in range(N)]
    ans = 1<<62
    for t in combinations(P, min(4, K)):
        xs, ys = zip(*t)
        xmin = min(xs)
        xmax = max(xs)
        ymin = min(ys)
        ymax = max(ys)
        area = (xmax-xmin) * (ymax-ymin)
        if ans < area:
            continue
        k = 0
        for x, y in P:
            if xmin <= x <= xmax and ymin <= y <= ymax:
                k += 1
        if k >= K:
            ans = area
    print(ans)

main()