Coin Rows
medium
Alice and Bob are playing a game on a matrix, consisting of 2 rows and m columns. The cell in the ith row in the jth column contains a[i][j] coins in it. Initially, both Alice and Bob are standing in a cell (1,1). They are going to perform a sequence of moves to reach a cell (2,m). The moves allowed are right and down one step. First, Alice makes all her moves until she reaches (2,m). she collects the coins in all cells she visit (including the starting cell). When Alice finishes, Bob starts his journey. He also performs the moves to reach (2,m) and collects the coins in all cells that he visited, but Alice didn't. The score of the game is the total number of coins Bob collects. Alice wants to minimize score of the game. Bob wants to maximize score of the game. What will be the score of the game if both players play optimally?
Constraints
1 <= t <= 100 1 <= m <= 10001 1 <= a[i][j] <= 10000
Format
Input
The first line contains a single integer t, number of test cases. The first line of the testcase contains a single integer m, the number of column in the matrix. The ith of the next 2 lines contain m integers. the number of coins in the cell in the ith row in the jth column of the matrix.
Output
For each testcase print a single integer the score of the game if both players play optimally.
Example
Sample Input
3
3
1 4 7
3 5 2
3
1 3 9
3 6 1
1
4
7
Sample Output
7
9
0
