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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