FJ and his cows enjoy playing a mental game. They write down the numbers from to 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 ) might go like this:
3 124
4 36
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 . 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: and the final sum.
输出格式
Line 1: An ordering of the integers 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.
