#include <iostream>
#include <algorithm>
#include <vector>
#include <map>
#include <set>
#include <cmath>
#include <array>
#include <string>
#include <cstdio>
#include <iterator>
#include <unordered_set>
#include <cstdint>
using namespace std;

template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) { return os << '(' << p.first << ", " << p.second << ')'; }
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type> ostream& operator<<(ostream &os, const T_container &v) { os << '{'; string sep; for (const T &x : v) os << sep << x, sep = ", "; return os << '}'; }
void dbg_out() { cout << endl; }
template<typename Head, typename... Tail> void dbg_out(Head H, Tail... T) { cout << ' ' << H; dbg_out(T...); }
#ifdef LOCAL
#define dbg(...) cout << "(" << #__VA_ARGS__ << "):", dbg_out(__VA_ARGS__)
#else
#define dbg(...)
#endif

/*

notes:

int64_t
stoi(string s) -> string to int
to_string() -> int (or else) to string

vector declaration:
vector<ll> v(n, 0)
vector<vector<ll>> v(n, vector<ll>(n, 0));

{if statement} ? {truth value} : {false value}

set lower bound/upper bound:
 	// . . . m1 . . . d . . . . m2
    auto m1_it = b.lower_bound(d);
    advance(m1_it, -1);
    m1 = *m1_it;
	m2 = *b.upper_bound(d);

*/

typedef int64_t ll;

void solve() {
	ll n = 0;
	cin >> n;
	vector<ll> a(n, 0);
	vector<ll> b(n, 0);
	vector<ll> used(n, 0);
	ll minn = -1;
	for(ll i = 0; i < n; i++) {
		ll tmp;
		cin >> tmp;
		a[i] = tmp;
	}
	for(ll i = 0; i < n; i++) {
		ll tmp;
		if(i < n - 1) {
			cin >> tmp;
			b[i] = tmp;
		}
		ll currmaxx = a[i] + b[i];
		if(i > 0) {
			currmaxx += b[i-1];
		}
		if(minn == -1 || currmaxx < minn) {
			minn = currmaxx;
		}
	}

	// binaris kereses (yay)
	//cerr << "\n\nminn= " << minn;
	ll left = 0, right = minn;
	while(left < right) {
		//cerr << "\nleft=" << left;
		//cerr << "\nright=" << right;
		ll mid = left + (right - left + 1)/2;
		//cerr << "\nmid=" << mid;
		bool poss = true;

		ll prev = 0;
		for(ll i = 0; i < n; i++) {
			ll curr = a[i] + prev;
			if(curr >= mid) {
				prev = b[i];
				continue;
			}
			ll needed = mid - curr;
			if(needed > b[i]) {
				//cerr << "\nimpossible at " << i;
				poss = false;
				break;
			}else{
				prev = b[i] - needed;
			}
		}

		if(poss == true) {
			left = mid;
		}else{
			right = mid - 1;
		}
	}

	cout << left << "\n";
    
}

int main()
{
	std::ios_base::sync_with_stdio(false);

	ll tests = 0;
	cin >> tests;

	while(tests--)
	{
		solve();
	}

	return 0;
}