// author : greedyman shashank

#include <bits/stdc++.h>
using namespace std;
void fast()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    cout.tie(NULL);
}
#define int long long int
#define mod 1000000007
#define pb push_back
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define f(i, s, n) for (i = s; i < n; i++)
#define yes cout << "yes" << endl;
#define no cout << "no" << endl;
#define vi vector<ll>
#define vb vector<bool>
#define pii pair<ll, ll>
#define vpi vector<pii>
#define umi unordered_map<ll, ll>
#define mi map<ll, ll>
#define si set<ll>

void init_code()
{
#ifndef ONLINE_JUDGE
    freopen("input.txt", "r", stdin);
    freopen("output.txt", "w", stdout);
    freopen("error.txt", "w", stderr);
#endif // ONLINE_JUDGE
}

// fuck the implimentation im bad
// good luck tho for next contst

bool func(int i, int par, int pref, vector<vector<int>> &v, vector<int> &a, int req)
{

    int x = a[i] + pref;
    if(x < -2e9 || pref < -2e9) {
        return false;
    }
    int sum = 0;
    //
    for (auto child : v[i])
    {
        if (child != par)
        {
            sum++;
        }
    }
    if (sum == 0)
    {
        if (x < 0)
            return false;
        else
            return true;
    }
    //
    if (i == 1)
    {
        if (x < req)
        {
            pref -= (req - x);
        }
    }
    else
    {
        if (x < 0)
        {
            pref += x;
        }
    }
    bool flag = true;
    for (auto child : v[i])
    {
        if (child != par)
        {
            flag = (flag && func(child, i, pref, v, a, req));
        }
    }
    return flag;
}

void solve()
{
    int n;
    cin >> n;
    vector<int> a(n + 1);
    int x, y;
    int i, j, sum = 0, ans = 0;
    f(i, 1, n + 1)
    {
        cin >> a[i];
    }
    vector<vector<int>> v(n + 1);
    f(i, 0, n - 1)
    {
        cin >> x;
        v[i + 2].pb(x);
        v[x].pb(i + 2);
    }
    int low = a[1];
    int high = 2e9;
    int mid;
    while (low <= high)
    {
        mid = (low + high) / 2;
        int req = mid;
        bool flag = func(1, -1, 0, v, a, req);
        if (flag)
        {
            ans = req;
            low = mid + 1;
        }
        else
            high = mid - 1;
    }
    cout << ans << endl;
    return;
}

signed main()
{
    init_code();
    fast();
    int t;
    cin >> t;
    while (t--)
    {
        solve();
    }
    return 0;
}