CF1373F.Network Coverage

The government of Berland decided to improve network coverage in his country. Berland has a unique structure: the capital in the center and $n$ cities in a circle around the capital. The capital already has a good network coverage (so the government ignores it), but the $i$-th city contains $a_i$ households that require a connection.

The government designed a plan to build $n$ network stations between all pairs of neighboring cities which will maintain connections only for these cities. In other words, the $i$-th network station will provide service only for the $i$-th and the $(i + 1)$-th city (the $n$-th station is connected to the $n$-th and the $1$-st city).

All network stations have capacities: the $i$-th station can provide the connection to at most $b_i$ households.

Now the government asks you to check can the designed stations meet the needs of all cities or not — that is, is it possible to assign each household a network station so that each network station $i$ provides the connection to at most $b_i$ households.

Berland 政府决定改善本国的网络覆盖。Berland 的地理结构十分独特：首都位于中心，周围呈环形分布着 $n$ 座城市。首都已有良好的网络覆盖（因此政府忽略首都），而第 $i$ 座城市中有 $a_i$ 户家庭需要接入网络。

政府设计了一套建设计划：在每对相邻城市之间建造 $n$ 个网络基站，每个基站仅为其所连接的两座城市提供服务。换言之，第 $i$ 个网络基站仅服务于第 $i$ 座城市和第 $(i + 1)$ 座城市（第 $n$ 个基站则连接第 $n$ 座城市和第 $1$ 座城市）。

所有网络基站均有容量限制：第 $i$ 个基站最多可为 $b_i$ 户家庭提供网络连接。

现在，政府请你判断：所设计的基站能否满足所有城市的网络需求？即，是否存在一种方案，将每一户家庭分配给某个网络基站，使得每个基站 $i$ 所服务的家庭数不超过其容量 $b_i$？

The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

The first line of each test case contains the single integer $n$ ($2 \le n \le 10^6$) — the number of cities and stations.

The second line of each test case contains $n$ integers ($1 \le a_i \le 10^9$) — the number of households in the $i$-th city.

The third line of each test case contains $n$ integers ($1 \le b_i \le 10^9$) — the capacities of the designed stations.

It's guaranteed that the sum of $n$ over test cases doesn't exceed $10^6$.

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

每个测试用例的第一行包含一个整数 $n$（$2 \le n \le 10^6$）—— 城市与电站的数量。

每个测试用例的第二行包含 $n$ 个整数（$1 \le a_i \le 10^9$）—— 第 $i$ 个城市中的家庭数量。

每个测试用例的第三行包含 $n$ 个整数（$1 \le b_i \le 10^9$）—— 设计的各电站的容量。

保证所有测试用例中 $n$ 的总和不超过 $10^6$。

For each test case, print YES, if the designed stations can meet the needs of all cities, or NO otherwise (case insensitive).

对于每个测试用例，如果所设计的车站能够满足所有城市的需求，则输出 YES，否则输出 NO（不区分大小写）。

In the first test case:

• the first network station can provide $2$ connections to the first city and $1$ connection to the second city;
• the second station can provide $2$ connections to the second city and $1$ connection to the third city;
• the third station can provide $3$ connections to the third city.

In the second test case:

• the $1$-st station can provide $2$ connections to the $1$-st city;
• the $2$-nd station can provide $3$ connections to the $2$-nd city;
• the $3$-rd station can provide $3$ connections to the $3$-rd city and $1$ connection to the $1$-st station.

In the third test case, the fourth city needs $5$ connections, but the third and the fourth station has $4$ connections in total.

在第一个测试用例中：

• 第一个网络基站可以向第一座城市提供 $2$ 个连接，向第二座城市提供 $1$ 个连接；
• 第二个基站可以向第二座城市提供 $2$ 个连接，向第三座城市提供 $1$ 个连接；
• 第三个基站可以向第三座城市提供 $3$ 个连接。

在第二个测试用例中：

• 第 $1$ 个基站可以向第 $1$ 座城市提供 $2$ 个连接；
• 第 $2$ 个基站可以向第 $2$ 座城市提供 $3$ 个连接；
• 第 $3$ 个基站可以向第 $3$ 座城市提供 $3$ 个连接，同时向第 $1$ 座城市提供 $1$ 个连接。

在第三个测试用例中，第四座城市需要 $5$ 个连接，但第三个和第四个基站总共仅有 $4$ 个连接。