Description

Solve the system of linear equations

subject to

x_i ≥ 0, ∀i = 1, 2, …, n.

Input

The input in is the following format with 1 ≤ m, n ≤ 100.

m	n
a11	a12	…	a1n	b1
a21	a22	…	a2n	b2
…	…	…	…	…
am1	am2	…	amn	bm

All numbers except m and n are real numbers.

Output

If any solutions exist, output one of them in the following format.

x1

x2

…

xn

Otherwise declare that the system is inconsistent by printing “impossible”. An special checker program that admits an absolute error of 10⁻¹⁰ is used to verify your results.

2 3
1 1 0 36
-1 1 -1 4

16
20
0

Source

, frkstyc