NSC#2339

NSC

1 second
64 megabytes
Hard

Recall that the least common multiple (LCM) of several numbers is the smallest natural number that is divisible by each of them.

You are given two numbers and . Try to find a set of distinct natural numbers such that their least common multiple is exactly . None of these numbers should be equal to .

Input

The first line contains two integers and (1 \leq N \leq 1000, 1 \leq K \leq 10^9), separated by a space.

Output

If such a set of numbers does not exist, print -1 on the first line of the output. Otherwise, print the required set of numbers separated by spaces. If there are several possible sets, output any one of them.

Examples

Example 1

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