Numbers
Numbers
Young Andrew is playing yet another numbers game. Initially, he writes down an integer a. Then, he chooses some divisor d1
of a (1 < d1
< a), erases a and writes a1
= a + d1
instead. Then,
he chooses some divisor d2
of a1
(1 < d2
< a1
), erases a1
and writes a2
= a1
+ d2
instead.
I.e., at any step he chooses some positive integer divisor of the current number, but not 1 and not the whole number, and increases the current number by it.
Is it possible for him to write number b if he started with number a?
Input
The only line contains two integers a and b (2 ≤ a < b ≤ 1012
).
Output
If there's no solution, output "Impossible" (without quotes) to the only line of output. If there's one, output the sequence of numbers written starting with a and ending with b, one per line. You're not asked to find the shortest possible sequence, however, you should find a sequence with no more than 500 numbers. It is guaranteed that if there exists some sequence for the given a and b, then there exists a sequence with no more than 500 numbers in it.
12 57
12 18 24 36 48 54 57
3 6
Impossible