Irrelevant Elements

Georgie is experimenting with a scheme for generating a pseudo-random integer in the range $0$ to $m-1$.

He first fixes $n$ and generates $n$ integers $a_1, a_2, \ldots, a_n$, each in the range $0$ to $m-1$. He then repeatedly replaces the current array with the array of sums of adjacent elements: from $a_1, a_2, \ldots, a_n$ he forms $a_1 + a_2, a_2 + a_3, \ldots, a_{n-1} + a_n$ (which has $n-1$ elements), and applies the same step again and again until a single number remains. That last number, taken modulo $m$, is the output of the scheme.

A weakness of this scheme is that the final result sometimes does not depend on some of the originally generated numbers. For example, when $n = 3$ and $m = 2$ the result never depends on $a_2$.

Call the $i$-th original element irrelevant if the final result never depends on $a_i$, no matter how the other numbers are chosen. Given $n$ and $m$, determine which elements are irrelevant.

A single line with two integers $n$ and $m$ ($1 \le n \le 100\,000$, $2 \le m \le 10^9$).

On the first line, print the number of irrelevant elements. On the second line, print in ascending order, separated by single spaces, the indices $i$ of all irrelevant elements. If there are no irrelevant elements, print an empty second line.