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.