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

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