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.
#include <bits/stdc++.h>
using namespace std;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  template <class c>
  debug& operator<<(const c&) {
    return *this;
  }
};
int main() {
  ios_base::sync_with_stdio(0);
  int T;
  cin >> T;
  for (int i = 1; i <= T; i++) {
    int n;
    cin >> n;
    int cities[n];
    int powers[n];
    for (int ii = 0; ii < n; ii++) {
      cin >> cities[ii];
    }
    for (int ii = 0; ii < n; ii++) {
      cin >> powers[ii];
    }
    bool ok = false;
    int min = 0;
    int max = powers[0];
    int check = 0;
    while (min <= max) {
      int mid = (min + max) / 2;
      int next = std::max(0, cities[1] - mid);
      int rest = powers[0] - mid;
      bool circ = true;
      for (int ii = 1; ii < n; ii++) {
        int can = powers[ii] - next;
        if (can < 0) {
          circ = false;
          break;
        }
        next = std::max(0, cities[(ii + 1) % n] - can);
        check++;
      }
      if (circ) {
        if (next <= rest) {
          ok = true;
          break;
        }
        if (max - min == 1) {
          break;
        }
        max = mid - 1;
      } else {
        min = mid + 1;
      }
    }
    if (ok) {
      cout << "YES" << endl;
    } else {
      cout << "NO" << endl;
    }
  }
}
