#include <stdio.h>
#include <assert.h>

#define NMAX 11111

int A[NMAX], B[NMAX], N;

void ReadInput() {
  scanf("%d", &N);
  assert(N >= 1 && N <= 10000);
  for (int i = 1; i <= N; i++) {
    scanf("%d", &B[i]);
    assert(B[i] >= 1 && B[i] <= (int) 1e6);
  }
  for (int i = 1; i <= N; i++) {
    scanf("%d", &A[i]);
    assert(A[i] >= 1 && A[i] <= (int) 1e6);
  }
}

int Solve() {
  long long sum = 0;
  for (int i = 1; i <= N; i++) sum += A[i] + B[i];
  if ((sum % N) != 0) {
    fprintf(stderr, "Fraud happened");
    return -1;
  }
  int ans = sum / N;
  int ok1 = false;
  int ok2 = false;
  for (int i = 1; i <= N; i++) {
    int x = A[i] + B[i];
    if (i < N) x += B[i + 1];
    if (x == ans) {
      A[i] = ans;
      B[i] = B[i + 1] = 0;
      continue;
    }
    if (x < ans) {
      ok1 = true;
      fprintf(stderr, "ok1 = %d\n", ok1);
      return -1;
    }
    if (A[i] + B[i] == ans) {
      A[i] = ans;
      B[i] = 0;
      continue;
    }
    if (i < N && A[i] + B[i + 1] == ans) {
      A[i] = ans;
      B[i + 1] = 0;
      A[i + 1] += B[i];
      B[i] = 0;
      continue;
    }
    if (i < N && A[i] == ans) {
      A[i + 1] += B[i];
      B[i] = 0;
      continue;
    }
    ok2 = true;
    fprintf(stderr, "ok2 = %d\n", ok2);
    return -1;
  }
  return ans;
}

int main() {
//  freopen("x.txt", "r", stdin);
  int T;
  scanf("%d", &T);
  while (T--) {
    ReadInput();
    printf("%d\n", Solve());
  }
  return 0;
}