#include <bits/stdc++.h>
#define pb push_back
#define fi first
#define se second
using namespace std; bool MEM;
using ll=long long; using ld=long double;
using pii=pair<int,int>; using pll=pair<ll,ll>;
const int I=1e9;
const ll J=1e18,N=3e5+7;
ll n,m,fa[N],a[N],sum,ans;
ll hl[N],ls[N],dep[N];
map<ll,ll> mp[N];
vector<ll> e[N];
vector<pll> qv[N];
void dfs(ll p,ll f) {
	hl[p]=ls[p]=0,dep[p]=dep[f]+1;
	for (ll i:e[p]) if (i!=f) {
		dfs(i,p);
		if (!ls[p]||hl[i]>hl[ls[p]]) ls[p]=i,hl[p]=hl[i]+1;
	}
}
void dfs1(ll p,ll f) {
	if (ls[p]) {
		dfs1(ls[p],p);
		mp[p].swap(mp[ls[p]]);
		for (ll i:e[p]) if (i!=f&&i!=ls[p]) {
			dfs1(i,p);
			for (pll j:mp[i]) mp[p][j.fi]+=j.se;
		}
		mp[p][dep[p]]+=a[p];
		for (pll o:qv[p]) {
			ll k=o.fi,w=o.se; auto it=mp[p].begin();
			while (it=mp[p].upper_bound(dep[p]+k),it!=mp[p].begin()) {
				it--;
				ll x=it->fi,y=it->se,z=min(y,w);
				y-=z,w-=z,ans+=z,mp[p][x]-=z;
				if (!y) mp[p].erase(x);
				if (!w) break;
			}
		}
	}
	else mp[p][dep[p]]=a[p];
//	printf("%lld\n",p);
//	for (pll i:mp[p]) printf("%lld %lld | ",i.fi,i.se); printf("\n");
}
void mian() {
	scanf("%lld%lld",&n,&m),sum=ans=0;
	for (ll i=1;i<=n;i++) e[i].clear(),qv[i].clear(),mp[i].clear();
	for (ll i=2;i<=n;i++) scanf("%lld",&fa[i]),e[fa[i]].pb(i);
	for (ll i=1;i<=n;i++) scanf("%lld",&a[i]),sum+=a[i];
	for (ll i=1,x,k,c;i<=m;i++) scanf("%lld%lld%lld",&x,&k,&c),qv[x].pb({k,c});
	dfs(1,0),dfs1(1,0);
	cout<<sum-ans<<"\n"; 
}
bool ORY; int main() {
	// while (1)
	 int t; for (scanf("%d",&t);t--;)
	mian();
	cerr<<"\n"<<abs(&MEM-&ORY)/1048576<<"MB";
	return 0;
}