Unnecessary Numbers

There is a sequence R[1], R[2], ..., R[N] of length N. Each element is an integer from 0 to M, inclusive.

Repeat the following transformation. If the current sequence has length L, replace it with the length L-1 sequence of adjacent sums: A[1]+A[2], A[2]+A[3], ..., A[L-1]+A[L]. Continue until only one number remains, then take that number modulo M as the final value.

An index i is unnecessary if it never affects the final value; that is, the final value is always the same no matter what value R[i] has.

Given N and M, write a program that finds how many indices are unnecessary and which indices they are.

The first line contains two integers N and M.

1 <= N <= 100,000

2 <= M <= 1,000,000,000

Print the number K of unnecessary indices on the first line.

On the second line, print the unnecessary indices in increasing order. If K = 0, the second line is empty.