#include<bits/stdc++.h>
#define ls (p<<1)
#define rs ((p<<1)|1)
#define ll long long
#define deb(x) cout << #x << ':' << x << '\n';
using namespace std;
const int N = 3e5+5;
inline int read(){
	int s = 0;char ch = getchar();
	while(!isdigit(ch))ch = getchar();
	while(isdigit(ch)){s = (s<<1)+(s<<3)+ch-'0';ch = getchar();}
	return s;
}
int hd[N],ect = 2,T,n,m,dis[N],son[N],a[N],id[N],tot,sz[N];
struct E{
	int v,nt;
}e[N];
void add(int u,int v){
	e[ect].v = v;
	e[ect].nt = hd[u];
	hd[u] = ect++;
}
struct Nd{
	int r,v;
};
vector<Nd> cm[N];
ll nf[N];
struct Sgt{
	struct T{
		int l,r,mid;
		ll tg,mn;
		bool ic;
		void mt(ll k,bool kd){
			if(kd){
				tg = mn = k;
				ic = 1;
			}else tg+=k,mn+=k;
		}
	};
	vector<T> t;
	Sgt(){}
	Sgt(int _sz):sz(_sz){
		t.resize((_sz<<2)+1);
		build(1,1,_sz);
	}
	ll v;int sz;bool oc;
//	T& operator[](int idx){
//		assert(idx>0&&idx<=mx);
//		return t[idx];
//	}
	void build(int p,int l,int r){
		t[p].l = l;t[p].r = r;
		t[p].mid = (l+r)>>1;
		t[p].tg = t[p].ic = 0;
		t[p].mn = -1;
		if(l==r)return;
		build(ls,l,t[p].mid);
		build(rs,t[p].mid+1,r);
	}
	inline void tag(int p){
		if(t[p].tg||t[p].ic){
			t[ls].mt(t[p].tg,t[p].ic);
			t[rs].mt(t[p].tg,t[p].ic);
			t[p].tg = t[p].ic = 0;
		}
	}
	void mdf(int p,int l,int r){
		if(l<=t[p].l&&t[p].r<=r){
//			deb("rg:");deb(l);deb(r);
			t[p].mt(v,oc);
			return;
		}
		tag(p);
		if(t[p].mid>=l)mdf(ls,l,r);
		if(t[p].mid<r)mdf(rs,l,r);
		t[p].mn = t[ls].mn;
	}
	void cg(int l,int r,ll cv,bool cc){
		v = cv,oc = cc;
		mdf(1,l,r);
	}
	int fd(int p,int l,int r,ll tv){
		if(l<=t[p].l&&t[p].r<=r){
			if(t[p].mn>tv)return 0;
			while(t[p].l!=t[p].r){
				tag(p);
//				deb(t[p].mn);
				if(t[rs].mn<=tv)p = rs;
				else p = ls;
			}
//			deb(t[p].mn);
			return t[p].l;
		}
		tag(p);
		int res = 0;
		if(t[p].mid<r){
			res = fd(rs,l,r,tv);
			if(res)return res;
		}
		if(t[p].mid>=l)return fd(ls,l,r,tv);
		else return 0;
	}
	void rev(int p,int to,ll cv,bool cc){
		if(t[p].l==t[p].r){
			if(cc)t[p].mn = cv;
			else t[p].mn+=cv;
			return;
		}
		tag(p);
		if(to<=t[p].mid)rev(ls,to,cv,cc);
		else rev(rs,to,cv,cc);
		t[p].mn = t[ls].mn;//写非递归形式，不更新mn...... 
	}
	ll getv(int to){
		int p = 1;
//		deb("!");
		while(t[p].l!=t[p].r){
			tag(p);
//			deb(t[p].l);deb(t[p].r);
			if(to<=t[p].mid)p = ls;
			else p = rs;
		}
		return t[p].mn;
	}
	void rb(int p){
		if(t[p].l==t[p].r){
			nf[t[p].l-1] = t[p].mn;
			return;
		}
//		deb(p);deb(t[p].tg);deb(t[p].ic);
		tag(p);
		rb(ls);rb(rs);
	}
	/*
	void prt(int x){
		rb(1);
		deb(x);
		for(int i = 0;i<sz;i++)printf("%lld ",nf[i]);
		puts("\n---------");
	}
	*/
};
vector<Sgt> sgs;
void dfs1(int p){
	if(!son[p]){
		ll s = 0;
		for(auto i:cm[p])s+=i.v;
		sgs[id[p]].rev(1,1,max(a[p]-s,0LL),1);
		return;
	}
	int pi = id[p];
	for(int i = hd[p];i;i = e[i].nt)dfs1(e[i].v);
//	deb(p);
//	sgs[pi].prt(p);
	for(int i = hd[p],vd;i;i = e[i].nt){
		if(e[i].v==son[p])continue;
		vd = dis[e[i].v];
		sgs[id[e[i].v]].rb(1);
		for(int j = 0;j<vd;j++)sgs[pi].rev(1,dis[p]-(vd-j),nf[j],0);
//		deb(e[i].v);
//		sgs[pi].prt(p);
	}
//	deb(p);
	sgs[pi].rev(1,dis[p],sgs[pi].getv(dis[p]-1)+a[p],1);
//	sgs[pi].prt(p);
	int l,r;
	ll v;
	for(auto nc:cm[p]){
		nc.r = min(nc.r+1,dis[p]);
		l = dis[p]-nc.r+1;
//		deb(nc.r);deb(nc.v);
		v = (l==1?0:sgs[pi].getv(l-1));
		r = sgs[pi].fd(1,l,dis[p],v+nc.v);
//		deb(l);deb(r);
		if(r)
			sgs[pi].cg(l,r,v,1);//不判r!=0!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
		else r = l-1;
		if(r<dis[p])sgs[pi].cg(r+1,dis[p],-nc.v,0);
//		sgs[pi].prt(p);
	}
//	deb(p);
}
void dfs0(int p){
	for(int i = hd[p];i;i = e[i].nt){
		dfs0(e[i].v);
		if(dis[e[i].v]>dis[son[p]])son[p] = e[i].v;
	}
	if(!son[p]){
		sz[tot] = 1;
		id[p] = tot++;
		dis[p] = 1;
	}else{
		id[p] = id[son[p]];
		sz[id[p]]++;
		dis[p] = dis[son[p]]+1;
	}
}
int main(){
//	freopen("hG.in","r",stdin);
//	freopen("cj.out","w",stdout);
	dis[0] = 0;
	T = read();
	while(T--){
//		n = read();printf("%d ",n);
		n = read();m = read();
//		printf("%d\n",n);
		ect = 2;
		memset(hd,0,4*n+4);
		memset(son,0,4*n+4);
		for(int i = 2,u;i<=n;i++){
			u = read();add(u,i);
		}
		for(int i = 1;i<=n;i++){
			cm[i].clear();
			a[i] = read();
		}
		for(int i = 1,p,r,v;i<=m;i++){
			p = read();r = read();v = read();
			cm[p].push_back(Nd{r,v});
		}
		tot = 0;
		dfs0(1);
		sgs.resize(tot);
		for(int i = 0;i<tot;i++)sgs[i] = Sgt(sz[i]);
		dfs1(1);
		printf("%lld\n",sgs[id[1]].getv(dis[1]));
	}
	return 0;
}
/*
1
5 5
1 1 2 2
2 4 4 3 3
5 2 1
1 3 3
1 1 5
3 3 5
1 1 2
2
*/