This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define ii pair<int,int>
#define fi first
#define se second
#define endl '\n'
#define puf push_front
#define pof pop_front
#define pub push_back
#define pob pop_back
#define lb lower_bound
#define ub upper_bound
#define rep(x,s,e) for (int x=(s)-((s)>(e));x!=(e)-((s)>(e));((s)<(e))?x++:x--)
#define all(x) (x).begin(),(x).end()
#define sz(x) (int) (x).size()
mt19937 rng(chrono::system_clock::now().time_since_epoch().count());
const int MOD=1000000007;
int qexp(int b,int p){
	int res=1;
	while (p){
		if (p&1) res=res*b%MOD;
		b=b*b%MOD;
		p>>=1;
	}
	return res;
}
int n,m,k;
vector<int> al[65];
vector<int> pos[15];
int pp[65];
int d[65];
void dfs(int i,int p){
	pp[i]=p;
	for (auto it:al[i]){
		if (it==p) continue;
		d[it]=d[i]+1;
		dfs(it,i);
	}
}
struct UFDS{
	int p[65];
	
	void reset(){
		rep(x,0,65) p[x]=x;
	}
	
	int par(int i){
		if (p[i]==i) return i;
		else return p[i]=par(p[i]);
	}
	
	void unions(int i,int j){
		i=par(i),j=par(j);
		p[i]=j;
	}
} ufds;
signed main(){
	cin.tie(0);
	cout.tie(0);
	cin.sync_with_stdio(false);
	
	cin>>n>>m>>k;
	
	int a,b;
	rep(x,1,n){
		cin>>a>>b;
		al[a].pub(b);
		al[b].pub(a);
	}
	
	dfs(1,-1);
	
	rep(x,0,m){
		cin>>a>>b;
		
		while (a!=b){
			if (d[a]<d[b]) swap(a,b);
			pos[x].pub(a);
			a=pp[a];
		}
	}
	
	//rep(x,0,m){
		//for (auto it:pos[x]) cout<<it<<" "; cout<<endl;
	//}
	
	int ans=0;
	rep(mask,0,1<<m){
		ufds.reset();
		rep(bit,0,m) if (mask&(1<<bit)){
			for (auto it:pos[bit]) ufds.unions(pos[bit][0],it);
		}
		
		int cnt=0;
		rep(x,2,n+1) if (ufds.p[x]==x) cnt++;
		cnt=qexp(k,cnt);
		
		if (__builtin_parity(mask)) ans=(ans-cnt+MOD)%MOD;
		else ans=(ans+cnt)%MOD;
	}
	
	cout<<ans<<endl;
}
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