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.

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 $10^6$ .

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

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.