CF1555C.Coin Rows

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?

Alice 和 Bob 正在一张由 $2$ 行 $m$ 列组成的矩阵上进行一场游戏。第 $i$ 行第 $j$ 列的格子中包含 $a_{i, j}$ 枚硬币。

初始时，Alice 和 Bob 均位于格子 $(1, 1)$。他们将执行一系列移动，最终均到达格子 $(2, m)$。

允许的移动方式为：

• 向右移动 —— 从某个格子 $(x, y)$ 移动到 $(x, y + 1)$；
• 向下移动 —— 从某个格子 $(x, y)$ 移动到 $(x + 1, y)$。

首先，Alice 独自完成全部移动，直至抵达 $(2, m)$。她收集其路径上所有经过的格子（包括起始格子 $(1, 1)$）中的硬币。

Alice 完成后，Bob 开始他的行程。他同样通过移动抵达 $(2, m)$，并收集所有他经过但 Alice 未经过 的格子中的硬币。

本游戏的得分为 Bob 所收集的硬币总数。

Alice 希望最小化该得分；Bob 希望最大化该得分。若双方均采取最优策略，游戏的最终得分是多少？

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 $10^5$.

第一行包含一个整数 $t$（$1 \le t \le 10^4$）——测试用例的数量。

接下来是 $t$ 个测试用例的描述。

每个测试用例的第一行包含一个整数 $m$（$1 \le m \le 10^5$）——矩阵的列数。

接下来两行中的第 $i$ 行包含 $m$ 个整数 $a_{i,1}, a_{i,2}, \dots, a_{i,m}$（$1 \le a_{i,j} \le 10^4$）——矩阵中第 $i$ 行、第 $j$ 列单元格内的硬币数量。

所有测试用例的 $m$ 值之和不超过 $10^5$。

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

对于每个测试用例，输出一个整数——即双方均采取最优策略时游戏的得分。

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.

测试用例的路径如以下图片所示。爱丽丝的路径用红色表示，鲍勃的路径用蓝色表示。