# POJ3187 Backward Digit Sums

## Description

FJ and his cows enjoy playing a mental game. They write down the numbers from 1 to N (1 <= N <= 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:

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.

## 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 one that is lexicographically least, i.e., that puts smaller numbers first.

## Hint

Explanation of the sample:

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

## Analysis

1. 全排列从字典序最小开始枚举这样的数列。
2. 每个数列叠加到最后成一个数，其实每个数字用到的个数是杨辉三角形。
3. 预先存 10 以内的杨辉三角形，直接与数组相乘求和即可。
# POJ