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.

Input

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 $10^6$.

Output

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

见题面 Input 部分

见题面 Output 部分

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.