#include<cstdio>

#include<algorithm>

using namespace std;

const int N=100010,M=262150;

int Case,cas,n,m,q,i,op,x,y,z;

int g[N],v[N<<1],nxt[N<<1],ed;

int size[N],son[N],f[N],d[N],st[N],top[N],dfn;

int val[M];

int ans;

struct E{int x,y,z,w;}e[N];

inline bool cmp(const E&a,const E&b){return d[a.z]<d[b.z];}

inline void addedge(int x,int y){v[++ed]=y;nxt[ed]=g[x];g[x]=ed;}

void dfs(int x){

    size[x]=1;

    for(int i=g[x];i;i=nxt[i])if(v[i]!=f[x]){

        f[v[i]]=x,d[v[i]]=d[x]+1;

        dfs(v[i]),size[x]+=size[v[i]];

        if(size[v[i]]>size[son[x]])son[x]=v[i];

    }

}

void dfs2(int x,int y){

    st[x]=++dfn;top[x]=y;

    if(son[x])dfs2(son[x],y);

    for(int i=g[x];i;i=nxt[i])if(v[i]!=son[x]&&v[i]!=f[x])dfs2(v[i],v[i]);

}

void build(int x,int a,int b){

    val[x]=0;

    if(a==b)return;

    int mid=(a+b)>>1;

    build(x<<1,a,mid),build(x<<1|1,mid+1,b);

}

void change(int x,int a,int b,int c,int p){

    val[x]+=p;

    if(a==b)return;

    int mid=(a+b)>>1;

    if(c<=mid)change(x<<1,a,mid,c,p);

    else change(x<<1|1,mid+1,b,c,p);

}

int ask(int x,int a,int b,int c,int d){

    if(c<=a&&b<=d)return val[x];

    int mid=(a+b)>>1,t=0;

    if(c<=mid)t=ask(x<<1,a,mid,c,d);

    if(d>mid)t+=ask(x<<1|1,mid+1,b,c,d);

    return t;

}

inline int lca(int x,int y){

    for(;top[x]!=top[y];x=f[top[x]])if(d[top[x]]<d[top[y]])swap(x,y);

    return d[x]<d[y]?x:y;

}

inline int chain(int x,int y){

    int t=0;

    for(;top[x]!=top[y];x=f[top[x]]){

        if(d[top[x]]<d[top[y]])swap(x,y);

        t+=ask(1,1,n,st[top[x]],st[x]);

    }

    if(d[x]<d[y])swap(x,y);

    t+=ask(1,1,n,st[y],st[x]);

    return t;

}

inline void gao(int x,int y,int z,int w){

    int t=chain(x,y);

    if(t>=w)return;

    w-=t;

    ans+=w;

    change(1,1,n,st[z],w);

}

int main(){

    scanf("%d",&Case);

    while(Case--){

        scanf("%d%d",&n,&m);

        for(i=1;i<n;i++){

            scanf("%d%d",&x,&y);

            addedge(x,y),addedge(y,x);

        }

        dfs(1);

        dfs2(1,1);

        build(1,1,n);

        for(i=1;i<=m;i++){

            scanf("%d%d%d",&x,&y,&e[i].w);

            e[i].x=x,e[i].y=y;

            e[i].z=lca(x,y);

        }

        sort(e+1,e+m+1,cmp);

        for(i=m;i;i--)gao(e[i].x,e[i].y,e[i].z,e[i].w);

        printf("%d\n",ans);

        for(i=0;i<=n;i++)g[i]=size[i]=son[i]=f[i]=d[i]=st[i]=top[i]=0;

        ed=dfn=ans=0;

    }

}