The Legend Was Invented, but Not the Name
How did the evil Chmyaaax become evil? The evil Chmyaaax was early a regular Max who was solving problems on Eolymp. He became evil because of a problem he couldn't solve. So, the legend about him was born, and although the truth about it remains unknown, the problem itself has survived. So, here is Frus' record about this problem:
You are given two numbers and . You need to find an array of numbers such that the sum of the squares of these numbers is equal to , and the sum of the cubes is equal to . Formally, you need to find any array of numbers such that:
where is the number of elements in this array.
Input
The first and only line contains two integers and ().
Output
In the first line, you need to output only one integer — the number of distinct elements in the array .
In the next lines you need to output the information about the array in the following form:
That means that there are elements in the array that are equal to .
All 's need to be pairwise distinct.
If there are multiple answers, you can output any of them.
If there are no needed arrays, you need to output .
Examples
Note
In the first example, there are elements equal to and element equal to . This way, the sums are following:
In the second example, there are 's and entry of each number from to :
In the third sample, it can be shown that there are no arrays that would satisfy the conditions.
Scoring
( points): ;
( points): ;
( points): ;
( points): no additional constraints.