#include <stdio.h>

#define NMAX 11111

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

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

int Solve() {
	long long sum = 0;
	for (int i = 1; i <= N; i++) sum += A[i] + B[i];
	if ((sum % N) != 0) return -1;
	int ans = sum / N;
	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) 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;
		}
		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;
}