[USACO06FEB]Backward Digit Sums G/S

题目描述

`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\$

输入输出样例

输入样例 #1

``4 16``

输出样例 #1

``3 1 2 4``