A system of linear equations is a collection of linear equations involving the same set of variables. A general system of $m$ linear equations with $n$ unknowns can be written as:

$${\displaystyle \begin{array}{rlrlrlrlrlrlrl}{a}_{11}{x}_1& & +& & a_{12}{x}_2& & +\cdots +& & a_{1n}{x}_n& & =& & & b_1\\ a_{21}{x}_1& & +& & a_{22}{x}_2& & +\cdots +& & a_{2n}{x}_n& & =& & & b_2\\ ⋮& & & & ⋮& & & & ⋮& & & & & ⋮\\ a_{m1}{x}_1& & +& & a_{m2}{x}_2& & +\cdots +& & a_{mn}{x}_n& & =& & & b_m.\end{array}}$$

Here, $x_1,x_2,\dots ,x_n$ are the unknowns, $a_{11},a_{12},\dots ,a_{mn}$ are the coefficients of the system, and $b_1,b_2,\dots ,b_m$ are the constant terms. (Source: Wikipedia)

Write a program that solves a system of linear equations with a maximum of $100$ equations and variables.

Input Specification

Line $1$ of the input contains integers $n$ and $m$ $(1\le n,m\le 100)$, indicating the number of variables to solve for and the number of equations in the system.
The next $m$ lines will each contain $n+1$ integers, where the first $n$ integers are the coefficients of the equation and the last integer is the constant term.
Every number in the input is guaranteed to have absolute value at most ${10}^6$.

It is guaranteed that the input is generated randomly. Specifically, for each test case, $n$ and $m$ will be picked arbitrarily, and so will two other integers, $l$ and $r$. Then, all other values in the input will be integers picked uniformly at random between $l$ and $r$.

Output Specification

If the system can be solved, output $n$ lines, the values of the unknowns $x_1,x_2,\dots ,x_n$. Your solution will be considered correct if each value has at most ${10}^{-5}$ absolute or relative error. If there are no solutions to the system, or if there are infinite solutions to the system, output NO UNIQUE SOLUTION.

Sample Input 1

2 2
1 3 4
2 3 6

Sample Output 1

2
0.66667

Explanation for Sample Output 1

This asks for the solution(s) for $x$ in the system:

$${\displaystyle \{\begin{array}{l}x+3y=4\\ 2x+3y=6\end{array}}$$

Solving for $x$ in the first equation gives $x=4-3y$. Substituting this into the $2$-nd equation and simplifying yields $3y=2$.
Solving for $y$ yields $y=\frac{2}{3}$. Substituting $y$ back into the first equation and solving for $x$ yields $x=2$.
Therefore the solution set is the single point $(x,y)=(2,\frac{2}{3})$.

Sample Input 2

2 3
6 2 2
12 4 8
6 2 4

Sample Output 2

NO UNIQUE SOLUTION

Explanation for Sample Output 2

All of the lines are parallel. Therefore, the system of equations cannot be solved.