Game with Strings

Limits: 2 sec., 256 MiB

Today Zenyk and Marichka have a game night, and they decided to play the following interesting game. Marichka writes down on two long pieces of paper strings \(s\) and \(t\), which consist of characters A and B. The goal for Zenyk is to cut out exactly \(|t|\) characters from \(s\) in such a way that the following two conditions are fulfilled:

1. The cut out characters make up string \(t\), if placed in the same order as in \(s\).

2. The remaining parts of \(s\) must be of form AA..A or BB..B. In other words, there should be no part that contains both A and B at the same time.

You are given two string \(s\) and \(t\). Help Zenyk achieve the goal of the game.

Input

The first line contains string \(s\), and the second line contains string \(t\). Both strings consist only of A and B characters.

Output

On the first line print "YES" if it is possible to achieve the goal, and "NO" otherwise (without quotes). In case of a positive answer, on the next line print \(|t|\) distinct integers in increasing order, which are the positions of characters that Zenyk will cut out from \(s\) (1-based index). If multiple answers exit, you may print any one of them.

Constraints

\(1 \le |t| \le |s| \le 10^5\).

Samples

Input (stdin) сopy	Output (stdout) сopy
AABBBAABBBABBB ABBA	YES 2 5 8 11

Input (stdin) сopy	Output (stdout) сopy
ABABABAB ABBA	NO

Notes

In the first sample, after cutting out the given characters, the following parts are left out: A, BB, AA, BB, BBB. None of them contain both A and B at the same time.