This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
// Judges with GCC >= 12 only needs Ofast
// #pragma GCC optimize("O3,no-stack-protector,fast-math,unroll-loops,tree-vectorize")
// MLE optimization
// #pragma GCC optimize("conserve-stack")
// Old judges
// #pragma GCC target("sse4.2,popcnt,lzcnt,abm,mmx,fma,bmi,bmi2")
// New judges. Test with assert(__builtin_cpu_supports("avx2"));
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma,tune=native")
// Atcoder
// #pragma GCC target("avx2,popcnt,lzcnt,abm,bmi,bmi2,fma")
#include<bits/stdc++.h>
using namespace std;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
uniform_real_distribution<> pp(0.0,1.0);
#define int long long
#define ld long double
#define pii pair<int,int>
#define piii pair<int,pii>
#define fi first
#define se second
const int inf=1e18;
const int mod=1e9+7;
const int maxn=105;
const int maxq=500005;
const int maxl=20;
const int maxa=1000005;
int power(int a,int n){
int res=1;
while(n){
if(n&1) res=res*a%mod;
a=a*a%mod;n>>=1;
}
return res;
}
vector<pii> edge[maxn];
vector<int> x[maxn];
int n,m,k;
bool dfs(int u,int par,int s,int id){
bool ok=(u==s);
for(pii v:edge[u]){
if(v.first==par) continue;
if(dfs(v.first,u,s,id)){
x[id].push_back(v.second);
ok=true;
}
}
return ok;
}
int cnt=0,par[maxn],r[maxn];
int findpar(int u){
if(u!=par[u]) return par[u]=findpar(par[u]);
return u;
}
void unions(int u,int v){
u=findpar(u);v=findpar(v);
if(u==v) return;
if(r[u]<r[v]) swap(u,v);
par[v]=u;r[u]+=r[v];cnt--;
}
void add(int p){
for(int j=0;j<(int)x[p].size()-1;j++) unions(x[p][j],x[p][j+1]);
}
void solve(){
cin >> n >> m >> k;
for(int i=1;i<n;i++){
int u,v;cin >> u >> v;
edge[u].push_back({v,i});
edge[v].push_back({u,i});
}
for(int i=0;i<m;i++){
int u,v;cin >> u >> v;
dfs(u,0,v,i);
}
int ans=0;
for(int i=0;i<(1<<m);i++){
cnt=n-1;
for(int j=1;j<n;j++){par[j]=j;r[j]=1;}
for(int j=0;j<m;j++){
if(i&(1<<j)) add(j);
}
if(__builtin_popcount(i)&1) ans=(ans-power(k,cnt)+mod)%mod;
else ans=(ans+power(k,cnt))%mod;
}
cout << ans << '\n';
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(NULL);cout.tie(NULL);
int test=1;//cin >> test;
while(test--) solve();
}
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