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F. Network Coverage

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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).

Example

Input

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

Output

YES YES NO YES YES

Note

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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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