Description

ljcc and his junior schoolmate are playing a game. The game has a total of $n$ rounds. Winning in the $i$-th round gives $i$ points. There are no draws.

Now you are given the scores of ljcc and the schoolmate. Determine whether there exists a valid plan that matches the current scores.

Input Format

Read from standard input.

Input one line with two integers $a,b$, representing the scores of ljcc and the schoolmate.

Output Format

Write to standard output.

If there is a solution, output one valid solution in one line. The first number represents that the game has played a total of $n$ rounds. Then output several numbers indicating in which rounds ljcc won. Separate every two numbers by a single space, and there must be no trailing spaces at the end of the line. If there is no valid solution, output No.

10 5

5 1 2 3 4

Hint

Due to SPJ issues, it is forbidden to output trailing spaces or extra newlines.

Constraints: $a,b\le 2^{31}-1$, $1\le n\le 10^5$.

Copyright Information

From THUPC (THU Programming Contest, Tsinghua University Programming Contest) 2017.

Translated by ChatGPT 5