Coin Rows

题意翻译

Alice 和 Bob 在一个 $2 \times m$ 的矩形上玩游戏，矩形的每一个格子上都有一个数 $a_{i,j}$ Alice 和 Bob 一开始站在左上角格子 (1,1) 上，每个人都**只能向下或者向右**移动，直到移动到终点 $(2,m)$ 上，经过一个格子时会取走格子上的数，赢得相应的得分 Alice 首先开始移动，**Bob 不能取走 Alice 已经取走的数** Alice 期望最小化 **Bob 的得分**，Bob 则希望最大化**自己的得分** 请输出 Bob 的最大得分

题目描述

Alice and Bob are playing a game on a matrix, consisting of $ 2 $ rows and $ m $ columns. The cell in the $ i $ -th row in the $ j $ -th 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 possible moves are: - Move right — from some cell $ (x, y) $ to $ (x, y + 1) $ ; - Move down — from some cell $ (x, y) $ to $ (x + 1, y) $ . 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 the score. Bob wants to maximize the score. What will the score of the game be if both players play optimally?

输入输出格式

输入格式

The first line contains a single integer $ t $ ( $ 1 \le t \le 10^4 $ ) — the number of testcases. Then the descriptions of $ t $ testcases follow. The first line of the testcase contains a single integer $ m $ ( $ 1 \le m \le 10^5 $ ) — the number of columns of the matrix. The $ i $ -th of the next $ 2 $ lines contain $ m $ integers $ a_{i,1}, a_{i,2}, \dots, a_{i,m} $ ( $ 1 \le a_{i,j} \le 10^4 $ ) — the number of coins in the cell in the $ i $ -th row in the $ j $ -th column of the matrix. The sum of $ m $ over all testcases doesn't exceed $ 10^5 $ .

输出格式

For each testcase print a single integer — the score of the game if both players play optimally.

输入输出样例

输入样例 #1

3
3
1 3 7
3 5 1
3
1 3 9
3 5 1
1
4
7

输出样例 #1

7
8
0

说明

The paths for the testcases are shown on the following pictures. Alice's path is depicted in red and Bob's path is depicted in blue.