ljcc and his junior are playing a game consisting of $n$ rounds. Winning the $i$-th round awards $i$ points, and there are no draws.

Given the total scores of ljcc and his junior, determine if there exists a valid scenario that results in these scores.

Input

The input consists of a single line containing two integers $a$ and $b$, representing the scores of ljcc and his junior, respectively.

Output

If a solution exists, output a valid configuration on a single line. The first number represents the total number of rounds $n$, followed by the indices of the rounds that ljcc won. Separate each number with a single space, and do not include trailing spaces at the end of the line. If no valid solution exists, output No.

Examples

Example 1 Input

10 5

Example 1 Output

5 1 2 3 4

Subtasks

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