CF1264B.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?

如果任意两个相邻数字之间的差的绝对值等于 $1$，则称该整数序列为“优美的”。更准确地说，序列 $s_1, s_2, \ldots, s_{n}$ 是优美的，当且仅当对所有 $1 \leq i \leq n - 1$，均有 $|s_i - s_{i+1}| = 1$。

Trans 拥有 $a$ 个数字 $0$、$b$ 个数字 $1$、$c$ 个数字 $2$ 和 $d$ 个数字 $3$。他希望用全部这 $a + b + c + d$ 个数字构造一个优美的序列。

然而，这一任务并不简单，Trans 未能成功完成。你能否帮帮他？

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

唯一的一行输入包含四个非负整数 $a$、$b$、$c$ 和 $d$（满足 $0 \lt a+b+c+d \leq 10^5$）。

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.

如果无法构造出满足上述约束条件的优美序列，则在一行中输出 "NO"（不带引号）。

否则，在第一行输出 "YES"（不带引号）；在第二行输出 $a + b + c + d$ 个整数，用空格分隔——一个优美序列。其中应恰好包含 $a$ 个 $0$、$b$ 个 $1$、$c$ 个 $2$ 和 $d$ 个 $3$。

若存在多个合法答案，输出任意一个即可。

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.

在第一个测试中，很容易看出该序列是优美的，因为任意两个相邻数字之间的差均为 $1$。此外，恰好有两个数字等于 $0$、$1$、$2$，且恰好有一个数字等于 $3$。

可以证明，在第二个和第三个测试中无法构造出优美的序列。