This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
/*input
4 3 3
1 2
2 3
4 2
1 4
1 3
4 3
*/
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
//#pragma GCC optimize("unroll-loops,no-stack-protector")
//order_of_key #of elements less than x
// find_by_order kth element
using ll = long long;
using ld = long double;
using pii = pair<ll,ll>;
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> indexed_set;
#define f first
#define s second
#define pb push_back
#define REP(i,n) for(int i=0;i<n;i++)
#define REP1(i,n) for(int i=1;i<=n;i++)
#define FILL(n,x) memset(n,x,sizeof(n))
#define ALL(_a) _a.begin(),_a.end()
#define sz(x) (int)x.size()
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define MP make_pair
const ll INF64=4e17;
const int INF=0x3f3f3f3f;
const ll MOD=1e9+7;
const ld PI=acos(-1);
const ld eps=1e-9;
#define lowb(x) x&(-x)
#define MNTO(x,y) x=min(x,(__typeof__(x))y)
#define MXTO(x,y) x=max(x,(__typeof__(x))y)
template<typename T1,typename T2>
ostream& operator<<(ostream& out,pair<T1,T2> P){
out<<P.f<<' '<<P.s;
return out;
}
template<typename T>
ostream& operator<<(ostream& out,vector<T> V){
REP(i,sz(V)) out<<V[i]+1<<((i!=sz(V)-1)?" ":"");
return out;
}
ll mult(ll a,ll b){
return ((a%MOD)*(b%MOD))%MOD;
}
ll mypow(ll a,ll b){
if(b<=0) return 1;
ll res=1LL;
while(b){
if(b&1) res=mult(res,a);
a=mult(a,a);
b>>=1;
}
return res;
}
const int maxn=1e3+5;
ll msk[maxn],mskk[maxn];
vector<pii> v[maxn];
vector<pii> pth;
int b;
int par[maxn];
int find(int u){
if(par[u]==u) return u;
return par[u]=find(par[u]);
}
void merge(int a,int b){
a=find(a),b=find(b);
if(a==b) return;
mskk[b]|=mskk[a];
par[a]=b;
}
ll dfs(int u,int p){
if(u==b) return 0;
for(auto x:v[u]){
if(x.f==p) continue;
ll z=dfs(x.f,u);
if(z!=-1){
return (z|(1LL<<x.s));
}
}
return -1;
}
int main(){
int n,m,k;
cin>>n>>m>>k;
REP(i,n-1){
int a,b;
cin>>a>>b;
--a,--b;
v[a].pb({b,i}),v[b].pb({a,i});
}
REP(i,m){
int a;
cin>>a>>b;
--a,--b;
msk[i]=dfs(a,-1);
}
int ans=0;
REP(i,(1<<m)){
vector<int> vv;
REP(j,m){
if(i&(1<<j)){
vv.pb(j);
}
}
REP(i,m) par[i]=i,mskk[i]=msk[i];
for(int a:vv){
for(int b:vv){
if(a>=b) continue;
if((msk[a]&msk[b])){
merge(a,b);
}
}
}
int cnt=n-1;
REP(j,m){
if(find(j)!=j or !(i&(1<<j))) continue;
cnt-=__builtin_popcountll(mskk[j]);
cnt++;
}
int z=mypow(k,cnt);
if(__builtin_popcount(i)%2) ans+=(MOD-z);
else ans+=z;
ans%=MOD;
}
cout<<ans<<'\n';
}
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