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.

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first line of each test case contains the single integer n (2 ≤ n ≤ 10^6) — the number of cities and stations.

The second line of each test case contains n integers (1 ≤ a_i ≤ 10^9) — the number of households in the i-th city.

The third line of each test case contains n integers (1 ≤ b_i ≤ 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.

inputFormat

Input

The first line contains a single integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The first line of each test case contains the single integer n (2 ≤ n ≤ 10^6) — the number of cities and stations.

The second line of each test case contains n integers (1 ≤ a_i ≤ 10^9) — the number of households in the i-th city.

The third line of each test case contains n integers (1 ≤ b_i ≤ 10^9) — the capacities of the designed stations.

It's guaranteed that the sum of n over test cases doesn't exceed 10^6.

outputFormat

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.

样例

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

</p>