Triple XOR

Limits: 2 sec., 512 MiB

This statement was translated automatically from Ukrainian.

You are given two positive integers \(m<n\). What is the maximum number of pairwise distinct integers that can be chosen from the interval \([m, n]\) such that the following condition is satisfied:

• There are no three distinct chosen numbers \(x, y, z\) such that \(x \oplus y \oplus z = 0\).

Recall that \(\oplus\) denotes the bitwise exclusive OR operation. For example, \(13 \oplus 6 = 11\), because in binary \(13 =\) 1101, and \(6 =\) 0110, so their \(\oplus\) is equal to 1011 \(= 11\).

Input

The only line of input contains two positive integers \(m, n\).

Output

In the first line, output the number \(k\) — the maximum number of integers that can be chosen satisfying the problem condition.

In the second line, output \(k\) pairwise distinct integers \(a_1, a_2, \ldots, a_k\), \(m \leq a_i \leq n\). They must satisfy the problem condition.

If there are several different ways to choose the maximum possible number of integers, find any of them.

Constraints

\(1 \leq m < n \leq 2\cdot 10^5\).

Samples

Input (stdin) сopy	Output (stdout) сopy
1 7	4 1 3 5 7

Input (stdin) сopy	Output (stdout) сopy
2024 2025	2 2025 2024

Notes

In the first example, it can be shown that choosing \(5\) numbers from the interval \([1, 7]\) in this way is impossible.

In the second example, among \([2024, 2025]\) there are no three distinct numbers, so the condition is satisfied automatically.