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:
def main():
    n, k, *xy = map(int, open(0).read().split())
    _x_ = sorted(xy[::2])
    ans = 4 * 10 ** 18
    for _x in _x_:
        for x_ in _x_[1:]:
            w = x_ - _x
            c = 0
            _h_ = []
            for x, y in zip(xy[::2], xy[1::2]):
                if _x <= x <= x_:
                    c += 1
                    _h_.append(y)

            if c >= k:
                _h_.sort()
                h = min(_h_[i + k - 1] - _h_[i] for i in range(c - k + 1))
                ans = min(ans, h * w)

    print(ans)


if __name__ == '__main__':
    main()