Sequence Construction with XOR Zero

Given two integers s and m, you are to construct a sequence a with an arbitrary length n (subject to 1 ≤ n ≤ m) satisfying the following conditions:

• Each element a_i must satisfy 1 ≤ ai ≤ s.
• The sum of all elements is exactly s, i.e.
  \(a_1+a_2+\cdots+a_n=s\).
• The bitwise XOR of all elements is 0, i.e.
  \(S(a)=a_1\oplus a_2\oplus\cdots\oplus a_n=0\). (Here, \(\oplus\) denotes the bitwise XOR operation.)

If it is possible to construct such a sequence, output any valid sequence; otherwise, output -1. Note that if n=1 then the only possibility is a₁=s but then \(S(a)=s\), which is 0 only when s=0. Thus, for any s ≥ 1 a valid sequence exists if and only if m ≥ 2 and s is even. A simple valid construction in this case is to take n = 2 and let a₁ = a₂ = s/2.

inputFormat

The input consists of two space-separated integers s and m on one line.

Constraints:

• 1 ≤ s ≤ 10⁹
• 1 ≤ m ≤ 10⁹

outputFormat

If a valid sequence exists, first output an integer n (the length of the sequence), followed by a line with n space-separated integers representing the sequence. If no valid sequence exists, output a single integer -1.

sample

4 2

2
2 2