题目描述
Problem Statement
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.
Input
<dl> <dt>Input is given from Standard Input in the following format:</dt> <dt>N K</dt> <dt>x_1 y_1</dt> <dd>x_{N} y_{N}</dd> </dl>Output
Print the minimum possible area of a rectangle that satisfies the condition.
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)
Sample Input 1
4 4
1 4
3 3
6 2
8 1
Sample Output 1
21
One rectangle that satisfies the condition with the minimum possible area has the following vertices: (1,1), (8,1), (1,4) and (8,4).
Its area is (8-1) × (4-1) = 21.
Sample Input 2
4 2
0 0
1 1
2 2
3 3
Sample Output 2
1
Sample Input 3
4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999
Sample Output 3
3999999996000000001
Watch out for integer overflows.
输入格式
见题面 Input 部分
输出格式
见题面 Output 部分