A. Coprime Array
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Given two integers $$$s$$$ and $$$x$$$, find any shortest array such that the sum of its elements is $$$s$$$, and all elements are coprime to $$$x$$$.

Two integers are coprime if the only positive integer that divides both of them is $$$1$$$.

Input

The only line contains the integers $$$s$$$ and $$$x$$$ ($$$2 \leq s, x \leq 10^9$$$).

Output

If there is no array that satisfies the condition, print a single integer $$$-1$$$.

Otherwise, the first line should contain one integer $$$n$$$ ($$$1 \leq n \leq 10^6$$$) — the length of the array. The next line should contain $$$n$$$ space-separated integers — the array itself. The elements of the array should not exceed $$$10^9$$$ in absolute value.

If there are multiple possible answers, print any. We have a proof that if a solution exists, then there exists a solution satisfying the constraints above.

Examples
Input
9 6
Output
3
-7 -7 23
Input
14 34
Output
2
83 -69