E - K-colinear Line /

### 問題文

ただし、そのようなものが無数に存在する場合は Infinity を出力してください。

### 制約

• 1 \leq K \leq N \leq 300
• \lvert X_i \rvert, \lvert Y_i \rvert \leq 10^9
• i\neq j ならば X_i\neq X_j または Y_i\neq Y_j
• 入力はすべて整数

### 入力

N K
X_1 Y_1
X_2 Y_2
\vdots
X_N Y_N


### 入力例 1

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


### 出力例 1

6


x=0, y=0, y=x\pm 1, y=-x\pm 16 本の直線が条件をみたします。

よって、6 を出力します。

### 入力例 2

1 1
0 0


### 出力例 2

Infinity


Score : 500 points

### 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.

### 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.

### 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.

### 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.