Problem Description

There are $ n $ employees in a company.
The seats are arranged in a straight line, and employee numbers are assigned sequentially from one end of this line.
The company uses the following method to measure the abilities of its employees.

First, each employee submits a list of employees they think are excellent to the company.
Let $ N(i) $ be the list submitted by the $ i $th employee.
Since employees do not know much about those sitting far away, $ N(i) $ does not include employees whose seats are more than 10 desks apart.
(For any $x \in N(i)$, $|i - x| \leq 10$ holds)
After collecting all the lists, a graph is constructed with employees as vertices and the relationships of thinking someone is excellent as directed edges.
Then, the Page Rank on this graph is used as the measure of the employee's ability.
If $ PR(i) $ is the Page Rank of the $ i $th employee and $ M(i) $ is the set of employees the $ i $th employee thinks are excellent, the Page Rank satisfies the following equation:

Your task is to write a program to calculate the Page Rank for the company.

Input Format

The input is given in the following format:

$ n $ $ m $ $ a_1 $ $ b_1 $ $ ... $ $ a_m $ $ b_m $

• The first line contains an integer $ n $ ($1 \leq n \leq 10{,}000$), representing the number of employees, and an integer $ m $ ($1 \leq m \leq 10{,}000$), representing the number of relationships where one employee thinks another is excellent.
• The following $ m $ lines contain two integers $ a_i $, $ b_i $ ($1 \leq a_i, b_i \leq n, |a_i - b_i| \leq 10$), indicating that the $ a_i $th employee thinks the $ b_i $th employee is excellent.

Output Format

Output the Page Rank value for each employee on a single line.

The answer will be considered correct if the relative or absolute error is at most $ 10^{-6} $.

Sample Input and Output

Sample Input #1

3 6
1 2
1 3
2 1
2 3
3 1
3 2

Sample Output #1

1
1
1

Sample Input #2

3 4
1 2
1 3
2 1
3 1

Sample Output #2

1.473684210526316
0.7631578947368423
0.7631578947368423

Notes/Hints

Sample Explanation 2

In this case, there are 3 employees. The 1st employee thinks the 2nd and 3rd employees are excellent. The 2nd employee thinks the 1st employee is excellent. The 3rd employee thinks the 1st employee is excellent. Therefore, the Page Rank for each employee satisfies all the following conditions:
$PR(1) = 0.1 + 0.9 \left( \frac{PR(2)}{1} + \frac{PR(3)}{1} \right)$
$PR(2) = 0.1 + 0.9 \left( \frac{PR(1)}{2} \right)$
$PR(3) = 0.1 + 0.9 \left( \frac{PR(1)}{2} \right)$

见题面 Input 部分

见题面 Output 部分