[USACO06FEB]Backward Digit Sums G/S


`FJ` and his cows enjoy playing a mental game. They write down the numbers from $1$ to$ N(1 \le N \le 10)$ in a certain order and then sum adjacent numbers to produce a new list with one fewer number. They repeat this until only a single number is left. For example, one instance of the game (when $N=4$) might go like this: ```cpp 3 1 2 4 4 3 6 7 9 16 ``` Behind `FJ`'s back, the cows have started playing a more difficult game, in which they try to determine the starting sequence from only the final total and the number $N$. Unfortunately, the game is a bit above `FJ`'s mental arithmetic capabilities. Write a program to help `FJ` play the game and keep up with the cows. 有这么一个游戏: 写出一个$1$至$N$的排列$a_i$,然后每次将相邻两个数相加,构成新的序列,再对新序列进行这样的操作,显然每次构成的序列都比上一次的序列长度少$1$,直到只剩下一个数字位置。下面是一个例子: $3,1,2,4$ $4,3,6$ $7,9$ $16$ 最后得到$16$这样一个数字。 现在想要倒着玩这样一个游戏,如果知道$N$,知道最后得到的数字的大小$sum$,请你求出最初序列$a_i$,为$1$至$N$的一个排列。若答案有多种可能,则输出字典序最小的那一个。 管理员注:本题描述有误,这里字典序指的是$1,2,3,4,5,6,7,8,9,10,11,12$ 而不是$1,10,11,12,2,3,4,5,6,7,8,9$





输出包括$1$行,为字典序最小的那个答案。 当无解的时候,请什么也不输出。(好奇葩啊)


输入样例 #1

4 16

输出样例 #1

3 1 2 4


对于$40\%$的数据,$n≤7$; 对于$80\%$的数据,$n≤10$; 对于$100\%$的数据,$n≤12,sum≤12345$。