Background

Problem Description

Given integers $x,y$, construct an integer sequence of length at most $10^6$ such that its sum is $x$ and its sum of squares is $y$. It is guaranteed that a solution exists.

Input Format

One line with two integers $x,y$.

Output Format

The first line contains a non-negative integer $n$, indicating the length of the sequence you construct. It must satisfy $n\le 10^6$.

The second line contains $n$ integers, representing the sequence you constructed. If there are multiple solutions, output any one. All elements in the output sequence must be integers with absolute value at most $10^6$.

100 5000

2
50 50

0 5000

2
50 -50

Hint

This problem uses bundled tests.

Constraints:

• Subtask 1 (10pts): $y\le 10$.
• Subtask 2 (40pts): $x=0$.
• Subtask 3 (50pts): No special constraints.

For all testdata, $0\le |x|,y\le10^6$, and a solution is guaranteed to exist.

Translated by ChatGPT 5