#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
#define X first
#define Y second
#define pb push_back
#define SZ(a) ((int)a.size())
#define ALL(v) v.begin(), v.end()

const int N = 3e5 + 5;

ll a[N], d[N], h[N];
map<ll, ll> mp[N];
vector<int> v[N];
vector<pll> con[N];

void szdfs(int now) {
    h[now] = 0;
    for (int x : v[now])
        d[x] = d[now] + 1, szdfs(x), h[now] = max(h[now], h[x] + 1);
}

void dfs(int now) {
    map<ll, ll> res;
    for (int x : v[now]) {
        dfs(x);
        if (SZ(mp[x]) > SZ(res))
            mp[x].swap(res);
        for (auto [i, j] : mp[x])
            res[i] += j;
        mp[x].clear();
    }
    res[d[now]] = res[d[now] + 1] + a[now];
    res[d[now] + 1] = -a[now];
    for (auto [k, c] : con[now]) {
        // d[now] -= c, d[now] + min(k, h[now]) + 1 += c
        k = min(k, h[now]); 
        res[d[now]] -= c;
        auto [it, succ] = res.insert({d[now] + k + 1, c});
        if (!succ)
            it->Y += c;
        while (it->X != d[now] && it->Y >= 0) {
            prev(it)->Y += it->Y;
            it = prev(res.erase(it));
        }
    }
    mp[now].swap(res);
}


void solve() {
    int n, m;
    cin >> n >> m;
    for (int i = 1; i <= n; i++)
        mp[i].clear(), v[i].clear(), con[i].clear();
    for (int i = 2; i <= n; i++) {
        int p;
        cin >> p;
        v[p].pb(i);
    }
    for (int i = 1; i <= n; i++)
        cin >> a[i];
    for (int i = 1; i <= m; i++) {
        int x, k, c;
        cin >> x >> k >> c;
        con[x].pb({k, c});
    }
    d[1] = 0;
    szdfs(1);
    dfs(1);
    assert(SZ(mp[1]));
    cout << mp[1].begin()->Y << "\n";
}

int main() {
    ios::sync_with_stdio(0), cin.tie(0);
    int T;
    cin >> T;
    while (T--)
        solve();
}