sum it up

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 file 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 x1, . . . ,xn. t will be a positive integer less than 1000, n will be an integer between 1 and 12 (inclusive), and x1, . . . , xn will be positive integers less than 100. All numbers will be separated by exactly one space. The numbers in each list may be repetitions.

 

Output

For each test case, output the total way, if not output -1.

 

Sample

Input

4

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

20 10

1 2 3 4 5 6 7 8 9 10

 

Output

#1 4

#2 -1

#3 2

#4 31

 

Giải thích

#1

4

3+1

2+2

2+1+1

 

#3

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

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

 

#4

1+2+3+4+10

1+2+3+5+9

1+2+3+6+8

1+2+4+5+8

1+2+4+6+7

1+2+7+10

1+2+8+9

1+3+4+5+7

1+3+6+10

1+3+7+9

1+4+5+10

1+4+6+9

1+4+7+8

1+5+6+8

1+9+10

2+3+4+5+6

2+3+5+10

2+3+6+9

2+3+7+8

2+4+5+9

2+4+6+8

2+5+6+7

2+8+10

3+4+5+8

3+4+6+7

3+7+10

3+8+9

4+6+10

4+7+9

5+6+9

5+7+8