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:

$$\displaystyle \begin{alignat}{7} a_{11} x_1 &&\; + \;&& a_{12} x_2 &&\; + \cdots + \;&& a_{1n} x_n &&\; = \;&&& b_1 \\ a_{21} x_1 &&\; + \;&& a_{22} x_2 &&\; + \cdots + \;&& a_{2n} x_n &&\; = \;&&& b_2 \\ \vdots\;\;\; && && \vdots\;\;\; && && \vdots\;\;\; && &&& \;\vdots \\ a_{m1} x_1 &&\; + \;&& a_{m2} x_2 &&\; + \cdots + \;&& a_{mn} x_n &&\; = \;&&& b_m. \end{alignat}$$

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:

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

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.