A13165. Beautiful Sequence

An integer sequence is called beautiful if the difference between any two consecutive numbers is equal to $1$ . More formally, a sequence $s_1, s_2, \ldots, s_{n}$ is beautiful if $|s_i - s_{i+1}| = 1$ for all $1 \leq i \leq n - 1$ .

Trans has $a$ numbers $0$ , $b$ numbers $1$ , $c$ numbers $2$ and $d$ numbers $3$ . He wants to construct a beautiful sequence using all of these $a + b + c + d$ numbers.

However, it turns out to be a non-trivial task, and Trans was not able to do it. Could you please help Trans?

The only input line contains four non-negative integers $a$ , $b$ , $c$ and $d$ ( $0 < a+b+c+d \leq 10^5$ ).

If it is impossible to construct a beautiful sequence satisfying the above constraints, print "NO" (without quotes) in one line.

Otherwise, print "YES" (without quotes) in the first line. Then in the second line print $a + b + c + d$ integers, separated by spaces — a beautiful sequence. There should be $a$ numbers equal to $0$ , $b$ numbers equal to $1$ , $c$ numbers equal to $2$ and $d$ numbers equal to $3$ .

If there are multiple answers, you can print any of them.

In the first test, it is easy to see, that the sequence is beautiful because the difference between any two consecutive numbers is equal to $1$ . Also, there are exactly two numbers, equal to $0$ , $1$ , $2$ and exactly one number, equal to $3$ .

It can be proved, that it is impossible to construct beautiful sequences in the second and third tests.