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).
5 3 2 3 4 3 3 3 3 3 3 3 2 3 4 4 2 3 4 5 3 7 2 2 4 4 5 2 3 2 3 2 7 2 1 1 10 10
YES YES NO YES YES
In the first test case:
In the second test case:
In the third test case, the fourth city needs $$$5$$$ connections, but the third and the fourth station has $$$4$$$ connections in total.