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Equal Sum Partitions
Time Limit: 1000MSMemory Limit: 65536K
Total Submissions: 898Accepted: 648


An equal sum partition of a sequence of numbers is a grouping of the numbers (in the same order as the original sequence) in such a way that each group has the same sum. For example, the sequence:
2 5 1 3 3 7

may be grouped as:
(2 5) (1 3 3) (7)

to yield an equal sum of 7.

Note: The partition that puts all the numbers in a single group is an equal sum partition with the sum equal to the sum of all the numbers in the sequence.

For this problem, you will write a program that takes as input a sequence of positive integers and returns the smallest sum for an equal sum partition of the sequence.


The first line of input contains a single integer P, (1 ≤ P ≤ 1000), which is the number of data sets that follow. The first line of each data set contains the data set number, followed by a space, followed by
a decimal integer M, (1 ≤ M ≤ 10000), giving the total number of integers in the sequence. The remaining line(s) in the dataset consist of the values, 10 per line, separated by a single space. The last line in the dataset may contain less than 10 values.


For each data set, generate one line of output with the following values: The data set number as a decimal integer, a space, and the smallest sum for an equal sum partition of the sequence.

Sample Input

1 6 
2 5 1 3 3 7 
2 6 
1 2 3 4 5 6 
3 20 
1 1 2 1 1 2 1 1 2 1 
1 2 1 1 2 1 1 2 1 1

Sample Output

1 7
2 21
3 2


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