Bacteria#1487
In a beautiful glass flask, young biologist Anton has bacteria.
By adding various reagents to the flask, Anton can control the number of bacteria. If is a prime number, Anton can produce the substance C_pH_{2p+1}OH at home. When added to the flask, this substance reduces the number of bacteria by exactly times. If the number of bacteria is not divisible by , the effect of the substance is undefined, and the experiment loses scientific accuracy. Anton wants to avoid this, so he only applies the substance C_pH_{2p+1}OH when the number of bacteria is divisible by .
Additionally, Anton has an unlimited supply of lysergic acid diethylamide (C_{20}H_{25}N_{3}O) in his kitchen. When added to the flask, this substance squares the number of bacteria.
Anton wants to have bacteria in the flask. He wants to achieve this by adding substances to the flask the fewest number of times possible. Help him reach his goal.
The input contains two natural numbers and (1 \le n,\ m \le 10^9) — the initial and desired number of bacteria in Anton's flask.
If it is impossible to obtain exactly bacteria, print the word Impossible.
If the desired result is achievable, print the shortest sequence of substance additions that yields bacteria, in the following format: the addition of the substance C_pH_{2p+1}OH is encoded by the number , and the addition of C_{20}H_{25}N_{3}O by the number . Numbers should be separated by spaces and/or newlines.
If there are several shortest sequences of substance additions that result in bacteria, print any of them.
Example 1