Time Limit:3000ms Memory Limit:65536KB

Description

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.

Input

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.

Output

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

3
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

Hint


Author

Source