Resistance Is (Not) Futile!

Acme Circuit Manufacturers (ACM) has hired you to cut the number of resistors in the electrical circuits it mass-produces, which lowers manufacturing cost.

A resistor is a small part that goes into every electrical circuit. It regulates the flow of electrons (the current) through a circuit by converting electrical energy into heat and dissipating that heat in a controlled and quantified way. We call this energy conversion resistance. Resistance is measured in ohms. The higher the ohm value, the higher the resistance.

To decide how many resistors to use and which ones, you first fix how much current you want in a path of the circuit, and the potential energy needed to move electrons from one point of that path to another (the voltage). Current, voltage and resistance are tied together by a very simple formula known as Ohm's law.

$V = IR$

Here $V$ is voltage, $I$ is current and $R$ is resistance.

Say a given path in the circuit carries 44558 volts and needs 10 amperes of current. Rearranging Ohm's law to make $R$ the subject, that path needs a resistor of 4455.8 ohms. Problem solved, right?

Wrong.

ACM only assembles circuits, it does not manufacture the components. Resistors are no exception. Most electronics companies buy pre-manufactured resistors, so resistor values had to be standardised. ACM uses the E-12 range of resistors, named after the 12 base values that every resistor value in the range comes from.

10, 12, 15, 18, 22, 27, 33, 39, 47, 56, 68, 82

These 12 values are the first decade of E-12 resistor values, measured in ohms. The second decade is

100, 120, 150, 180, 220, 270, 330, 390, 470, 560, 680, 820

The third and later decades come from multiplying each base value by the appropriate power of 10.

The resistance of an E-12 resistor is usually only approximately equal to its nominal value, but ACM has found a supplier that guarantees exact resistances. ACM wants to combine these exact resistors to land close to the desired resistance while using as few resistors as possible. Resistors are always connected in series, so the resistance of a set of resistors is the sum of their resistances. ACM measures how close an approximation is with the error. If $R$ is the target resistance and $S$ is the sum of the chosen resistances, the error is the distance of the approximate value from the target value expressed as a percentage of the approximate value, that is $|R - S| \times 100 / S$ percent. This error has to be at most 1%.

For example, to approximate 4455.8 ohms you could pick

3900, 470, 82

They sum to 4452 ohms and the error is only $|4455.8 - 4452| \times 100 / 4452 = 0.085\%$, well inside the required 1%. A better choice is

3900, 560

The total of 4460 ohms is not as accurate as the previous choice, but the error is still well under 1% and this set uses one resistor fewer. On a large production run the cost of every resistor adds up.

Write a program that, given a voltage and a current, picks the best set of resistors that supplies the required resistance within the 1% error defined above.

The input contains a single test case.

The first line contains two integers $V$ and $I$, the voltage and the current. ($1 \le V \le 10^9$, $1 \le I \le 10^7$)

Print on one line the E-12 resistor values that approximate the target resistance with an error of at most 1% using the fewest resistors, from the largest value to the smallest, separated by spaces.

You can use the same resistor value more than once. If two or more sets with the same smallest number of resistors stay inside the error range, print the set whose sum is closest to the target value. If two sets sit at the same distance from the target value, print the set whose sum is smaller. If that still leaves a tie, print the set that is lexicographically least when its resistors are ordered from largest to smallest.

If no set of resistors reaches the target resistance under these rules, print Impossible instead.