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.
from sys import stdin, stdout

#  4  5  2  3
#  2  3  2  7
# -2 -2  0  4
#
#  3   3   3
#  2   3   4
# -1   0   1

#  2  3  4  5
#  3  7  2  2
#  1  4 -2 -3
if __name__ == '__main__':

    def network_coverage(n, a, b):
        l = 0
        h = min(a[0], b[-1]) + 1

        while l < h:
            take = (l + h)//2
            avail = take

            for i in range(n):
                need = max(0, a[i] - avail)

                if i < n-1:
                    if b[i] < need:
                        l = take + 1
                        break
                else:
                    if b[i] - take < need:
                        h = take
                        break
                    else:
                        return "YES"

                avail = b[i] - need

        return "NO"

    t = int(stdin.readline())
    for i in range(t):
        n = int(stdin.readline())
        a = list(map(int, stdin.readline().split()))
        b = list(map(int, stdin.readline().split()))

        stdout.write(network_coverage(n, a, b) + '\n')
