Axis-Parallel Rectangle

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

inputFormat

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}

outputFormat

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

样例

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

3999999996000000001