Sashko-Array Constructor

Input

The single line contains two integers $x$ (2 \le x \le 10^{9}) and $d$ (2 \le d \le 10^{9})

Output

If such an array does not exist, then output "$-1$".

Otherwise, in the first line, output the number $n$ (1 \le n \le 1000) — the minimal size of the array.

In the second line, output the numbers a_1,a_2,\dots,a_n (1 \le a_i \le d), which satisfy the condition.

If there are multiple correct answers, any of them are allowed.

It can be shown that the length of the optimal array always satisfies the constraint.

Examples

Note

In the first example, x=10 and d=5. You need to find an array with a product of $10$. The array "$5,2$" fits, because 5\times 2=10 and each number is not greater than $d$. It is impossible to make an array of size one, because then the only element should be equal to $x$, and in this test x>d.

Scoring

In this problem, there are conditional blocks. If your solution works correctly for certain constraints, it will receive a certain number of points. Note that the evaluation is still in the testing phase.

• ($37$ points): x,d \le 2 \cdot 10^{5};

• ($63$ points): without additional constraints.