P1118 [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.

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- 对于 $40\%$ 的数据，$1\le n\le 7$； - 对于 $80\%$ 的数据，$1\le n \le 10$； - 对于 $100\%$ 的数据，$1\le n \le 12$，$1\le sum\le 12345$。