## System Solver

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:

Here,

*x*are the unknowns,

_{1}, x_{2}, …, x_{n}*a*are the coefficients of the system, and

_{11}, a_{12}, …, a_{mn}*b*are the constant terms. (Source: Wikipedia)

_{1}, b_{2}, …, b_{m}Write a program that solves a system of linear equations with a maximum of 100 equations and variables.

### Input Format

Line 1 of the input contains integers `n` and `m` (1 ≤ `n, m` ≤ 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 fit in a 32-bit signed integer.

### Output Format

If the system can be solved, output `n` lines, the values of the unknowns *x _{1}, x_{2}, …, x_{n}*, accurate within ±10

^{-5}.

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

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

Solving for x in the first equation gives x = 4 - 3y. Substituting this into the 2nd equation and simplifying yields 3y = 2.

Solving for y yields y = ^{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, ^{2}⁄_{3}).

### Sample Input 2

2 3 6 2 2 12 4 8 6 2 4

### Sample Output 2

NO UNIQUE SOLUTION

### Explanation

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

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Best Solutions

**Point Value:** 20 (partial)

**Time Limit:** 2.00s

**Memory Limit:** 16M

**Added:** Jul 12, 2013

**Author:** Alex

**Languages Allowed:**

C++03, PAS, C, HASK, ASM, RUBY, PYTH2, JAVA, PHP, SCM, CAML, PERL, C#, C++11, PYTH3

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