搜索（DFS）

Sum It Up

Description

Given a specified total t and a list of n integers,
find all distinct sums using numbers from the list that add up to t. For
example, if t = 4, n = 6, and the list is [4, 3, 2, 2, 1, 1], then there are
four different sums that equal 4: 4, 3+1, 2+2, and 2+1+1. (A number can be used
within a sum as many times as it appears in the list, and a single number counts
as a sum.) Your job is to solve this problem in general.

Input

The input will contain one or more test cases, one per
line. Each test case contains t, the total, followed by n, the number of
integers in the list, followed by n integers x 1 , . . . , x n . If n = 0 it
signals the end of the input; otherwise, t will be a positive integer less than
1000, n will be an integer between 1 and 12 (inclusive), and x 1 , . . . , x n
will be positive integers less than 100. All numbers will be separated by
exactly one space. The numbers in each list appear in nonincreasing order, and
there may be repetitions.

Output

For each test case, first output a line containing
`Sums of‘, the total, and a colon. Then output each sum, one per line; if there
are no sums, output the line `NONE‘. The numbers within each sum must appear in
nonincreasing order. A number may be repeated in the sum as many times as it was
repeated in the original list. The sums themselves must be sorted in decreasing
order based on the numbers appearing in the sum. In other words, the sums must
be sorted by their first number; sums with the same first number must be sorted
by their second number; sums with the same first two numbers must be sorted by
their third number; and so on. Within each test case, all sums must be distinct;
the same sum cannot appear twice.

Sample Input

4 6 4 3 2 2 1 1

5 3 2 1 1

400 12 50 50 50 50 50 50 25 25 25 25 25 25

0 0

Sample Output

Sums of 4:

4

3+1

2+2

2+1+1

Sums of 5:

NONE

Sums of 400:

50+50+50+50+50+50+25+25+25+25

50+50+50+50+50+25+25+25+25+25+25

?