Problem Background

DPair plans to bring smiles to everyone with Midrash.

Since Lillia doesn't know what Midrash is, she intends to stop him.

To stop DPair, you need to craft a small aluminum hammer.

If you don't know how to craft a small aluminum hammer, you can refer to the video provided below the problem.

Alternatively, you can choose to solve the easy problem of this monthly competition.

Problem Description

Construct a sequence of positive integers \( a \) such that the product of all elements in \( a \) is \( n \) and the sum of all elements is \( k \). If no such sequence exists, output -1.

Input Format

A single line containing two positive integers \( n \) and \( k \).

Output Format

The first line contains an integer \( m \), representing the length of the sequence.
The next line contains \( m \) positive integers \( a_i \), representing the sequence. It is required that \( 1 \leq m \leq 1000 \) and \( 1 \leq a_i \leq 1000 \).
If there is no valid sequence, output -1 directly.

This problem uses a Special Judge. If there are multiple answers, any one of them will be accepted.

Sample Input and Output

Sample Input #1

67 68

Sample Output #1

2
1 67

Sample Input #2

100 1

Sample Output #2

-1

Sample Input #3

80 16

Sample Output #3

6
1 1 4 5 1 4

Notes

[Sample Explanation]

For the first sample, clearly \( 1 \times 67 = 67 \) and \( 1 + 67 = 68 \).
For the second sample, it can be proven that there is no valid solution.

[Data Range]

For 10% of the data, \( 1 \leq n, k \leq 3 \);
For 30% of the data, \( 1 \leq n, k \leq 10 \);
Additionally, 10% of the data have \( n = k \);
For 100% of the data, \( 1 \leq n, k \leq 100 \).

见题面 Input 部分

见题面 Output 部分