#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
using namespace __gnu_pbds;
#define int long long
typedef pair<int,int> pii;
typedef vector<int> vi;
typedef vector<pii> vii;
typedef vector<bool> vb;
typedef tree<pii,null_type,less<pii>,rb_tree_tag,
tree_order_statistics_node_update> oset;
#define fi first
#define se second
#define pb push_back
#define mid (l+r)/2
#define all(x) x.begin(),x.end()
#define FOR(i,a) for(int i=0;i<(a);i++)
#define FORE(i,a,b) for(int i=(a);i<(b);i++)
#define cont(x) for(auto el:x) cout<<el<<' ';cout<<endl;
#define contp(x) for(auto el:x) cout<<el.fi<<'-'<<el.se<<' ';cout<<endl;
#define sp <<" "<<
#define DEBUG(x) cout<<(#x) sp x<<endl
#define carp(a,b) (((a%MOD)*(b%MOD))%MOD)
#define topla(a,b) (((a%MOD)+(b%MOD))%MOD)
const int INF=1e18;
const int MAXN=65;
const int MAXK=10;
const int MOD=1e9+7;
int n,m,k;
vii adj[MAXN];
int up[MAXN][MAXK];
int dep[MAXN];
pii p[MAXN];
void dfs(int nd,int ata,int h){
dep[nd]=h;
for(auto [kom,ind]:adj[nd]){
if(kom==ata) continue;
p[kom]={nd,ind};
dfs(kom,nd,h+1);
}
}
void calc(){
memset(up,-1,sizeof up);
FORE(i,1,n+1){
up[i][0]=p[i].fi;
}
FORE(j,1,MAXK){
FORE(i,1,n+1){
if(up[i][j-1]==-1) continue;
up[i][j]=up[up[i][j-1]][j-1];
}
}
}
int lca(int a,int b){
//a altta olan, b üstte olan
if(dep[a]<dep[b]) swap(a,b);
for(int i=MAXK-1;i>=0;i--){
int tt=up[a][i];
if(tt==-1) continue;
if(dep[tt]>=dep[b]) a=tt;
}
if(a==b) return a;
for(int i=MAXK-1;i>=0;i--){
int bir=up[a][i];
int iki=up[b][i];
if(bir==-1 or iki==-1) continue;
if(bir!=iki){
a=bir;
b=iki;
}
}
return up[a][0];
}
int exp(int x,int us){
int res=1;
while(us>0){
if(us&1) res=carp(res,x);
x=carp(x,x);
us/=2;
}
return res;
}
int comp,edg;
int used[MAXN];
bool vis[MAXN][MAXN];
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
cout.tie(0);
cin>>n>>m>>k;
FOR(i,n-1){
int a,b;
cin>>a>>b;
adj[a].pb({b,i});
adj[b].pb({a,i});
}
p[1]={-1,-1};
dfs(1,-1,0);
calc();
vector<pair<pii,int>> tut;
FOR(i,m){
int a,b;
cin>>a>>b;
if(dep[a]<dep[b]) swap(a,b); //a altta olan
tut.pb({{a,b},lca(a,b)});
}
int ans=exp(k,n-1);
for(int i=1;i<(1<<m);i++){
int say=0;
FOR(j,n-1) used[j]=false;
FOR(j,m){
FOR(t,m){
vis[j][t]=false;
}
}
edg=comp=0;
for(int bt=0;bt<m;bt++){
if(i&(1<<bt)){
bool f=true;
int ata=tut[bt].se;
int x=tut[bt].fi.fi;
while(x!=ata){
if(!used[p[x].se]) edg++;
else{
if(!vis[bt][used[p[x].se]]){
vis[bt][used[p[x].se]]=true;
vis[used[p[x].se]][bt]=true;
comp--;
}
}
used[p[x].se]=bt;
x=p[x].fi;
}
x=tut[bt].fi.se;
while(x!=ata){
if(!used[p[x].se]) edg++;
else{
if(!vis[bt][used[p[x].se]]){
vis[bt][used[p[x].se]]=true;
vis[used[p[x].se]][bt]=true;
comp--;
}
}
used[p[x].se]=bt;
x=p[x].fi;
}
say++;
comp++;
}
}
int kalan=n-1-edg+comp;
int deg=exp(k,kalan);
//cout<<"here" sp edg sp comp sp kalan sp deg sp i sp say<<endl;
if(say%2==0) ans=topla(ans,deg);
else ans=topla(ans,MOD-deg);
}
cout<<ans<<endl;
}
