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:

    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.

输入格式

Line 1: Two space-separated integers: N and the final sum.

输出格式

Line 1: An ordering of the integers 1..N that leads to the given sum. If there are multiple solutions, choose the one that is lexicographically least, i.e., that puts smaller numbers first.

4 16

3 1 2 4

提示

• For $40\%$ of the data, $1\le n\le 7$;
• For $80\%$ of the data, $1\le n \le 10$;
• For $100\%$ of the data, $1\le n \le 12$, $1\le sum\le 12345$.