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.

Input

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

Output

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

Examples

Input 1

4 16

Output 1

3 1 2 4

There are other possible sequences, such as 3 2 1 4, but 3 1 2 4 is lexicographically smallest.

Problem by Harry Wiggins (2002).