CF1031C.Cram Time

In a galaxy far, far away Lesha the student has just got to know that he has an exam in two days. As always, he hasn't attended any single class during the previous year, so he decided to spend the remaining time wisely.

Lesha knows that today he can study for at most $a$ hours, and he will have $b$ hours to study tomorrow. Note that it is possible that on his planet there are more hours in a day than on Earth. Lesha knows that the quality of his knowledge will only depend on the number of lecture notes he will read. He has access to an infinite number of notes that are enumerated with positive integers, but he knows that he can read the first note in one hour, the second note in two hours and so on. In other words, Lesha can read the note with number $k$ in $k$ hours. Lesha can read the notes in arbitrary order, however, he can't start reading a note in the first day and finish its reading in the second day.

Thus, the student has to fully read several lecture notes today, spending at most $a$ hours in total, and fully read several lecture notes tomorrow, spending at most $b$ hours in total. What is the maximum number of notes Lesha can read in the remaining time? Which notes should he read in the first day, and which — in the second?

在遥远的银河系中，学生莱沙刚刚得知两天后他将有一场考试。和往常一样，他在过去一年中一节课也没有上过，因此他决定明智地利用剩下的时间。

莱沙知道今天他最多可以学习 $a$ 小时，而明天则有 $b$ 小时可用于学习。注意，在他的星球上，一天的小时数可能比地球上的更多。莱沙知道，他知识掌握的质量仅取决于他所阅读的讲义笔记的数量。他可以无限获取编号为正整数的讲义笔记，但他知道：阅读第 1 篇笔记需要 1 小时，阅读第 2 篇笔记需要 2 小时，依此类推。换言之，莱沙阅读编号为 $k$ 的笔记需要 $k$ 小时。莱沙可以按任意顺序阅读这些笔记，但不能在第一天开始阅读某篇笔记，又在第二天完成该笔记的阅读。

因此，莱沙必须在今天完整地阅读若干篇讲义笔记，总耗时不超过 $a$ 小时；并在明天完整地阅读若干篇讲义笔记，总耗时不超过 $b$ 小时。在剩余时间内，莱沙最多能阅读多少篇笔记？他第一天应阅读哪些笔记，第二天又应阅读哪些笔记？

The only line of input contains two integers $a$ and $b$ ($0 \leq a, b \leq 10^{9}$) — the number of hours Lesha has today and the number of hours Lesha has tomorrow.

输入仅包含一行，其中有两个整数 $a$ 和 $b$（$0 \leq a, b \leq 10^{9}$）——分别表示莱沙今天和明天拥有的小时数。

In the first line print a single integer $n$ ($0 \leq n \leq a$) — the number of lecture notes Lesha has to read in the first day. In the second line print $n$ distinct integers $p_1, p_2, \ldots, p_n$ ($1 \leq p_i \leq a$), the sum of all $p_i$ should not exceed $a$.

In the third line print a single integer $m$ ($0 \leq m \leq b$) — the number of lecture notes Lesha has to read in the second day. In the fourth line print $m$ distinct integers $q_1, q_2, \ldots, q_m$ ($1 \leq q_i \leq b$), the sum of all $q_i$ should not exceed $b$.

All integers $p_i$ and $q_i$ should be distinct. The sum $n + m$ should be largest possible.

第一行输出一个整数 $n$（$0 \leq n \leq a$）—— Lesha 第一天需要阅读的讲义数量。
第二行输出 $n$ 个互不相同的整数 $p_1, p_2, \ldots, p_n$（$1 \leq p_i \leq a$），且所有 $p_i$ 的和不超过 $a$。

第三行输出一个整数 $m$（$0 \leq m \leq b$）—— Lesha 第二天需要阅读的讲义数量。
第四行输出 $m$ 个互不相同的整数 $q_1, q_2, \ldots, q_m$（$1 \leq q_i \leq b$），且所有 $q_i$ 的和不超过 $b$。

所有整数 $p_i$ 和 $q_i$ 必须互不相同。$n + m$ 应尽可能大。

In the first example Lesha can read the third note in $3$ hours in the first day, and the first and the second notes in one and two hours correspondingly in the second day, spending $3$ hours as well. Note that Lesha can make it the other way round, reading the first and the second notes in the first day and the third note in the second day.

In the second example Lesha should read the third and the sixth notes in the first day, spending $9$ hours in total. In the second day Lesha should read the first, second fourth and fifth notes, spending $12$ hours in total.

在第一个例子中，莱沙可以在第一天用 3 小时阅读第三张笔记，第二天用 1 小时和 2 小时分别阅读第一张和第二张笔记，同样总共花费 3 小时。注意，莱沙也可以采用另一种方式：第一天阅读第一张和第二张笔记，第二天阅读第三张笔记。

在第二个例子中，莱沙应在第一天阅读第三张和第六张笔记，总共花费 9 小时；第二天应阅读第一张、第二张、第四张和第五张笔记，总共花费 12 小时。