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.