Problem Statement

You are given N points in the coordinate plane.
For each $1\leq i\leq N$, the i-th point is at the coordinates (X_i, Y_i).
Find the number of lines in the plane that pass K or more of the N points.
If there are infinitely many such lines, print Infinity.

Input

Input is given from Standard Input in the following format:
N K
X_1 Y_1
X_2 Y_2
$\vdots$
X_N Y_N

Output

Print the number of lines in the plane that pass K or more of the N points, or Infinity if there are infinitely many such lines.

Constraints

• $1 \leq K \leq N \leq 300$
• $\lvert X_i \rvert, \lvert Y_i \rvert \leq 10^9$
• $X_i\neq X_j$ or $Y_i\neq Y_j$, if $i\neq j$.
• All values in input are integers.

Sample Input 1

5 2
0 0
1 0
0 1
-1 0
0 -1

Sample Output 1

6

The six lines $x=0, y=0, y=x\pm 1$, and $y=-x\pm 1$ satisfy the requirement.
For example, x=0 passes the first, third, and fifth points.
Thus, 6 should be printed.

Sample Input 2

1 1
0 0

Sample Output 2

Infinity

Infinitely many lines pass the origin.
Thus, Infinity should be printed.

见题面 Input 部分

见题面 Output 部分