#include <bits/stdc++.h>
using namespace std;
#define task "main"
#define F first
#define S second
#define ii pair<int, int>
#define il pair<int, long long>
#define li pair<long long, int>
#define FOR(i, a, b) for(int i = (a); i <= (b); ++i)
#define FOD(i, b, a) for(int i = (b); i >= (a); --i)
template <class T1, class T2>
bool maximize(T1 &a, T2 b){
if (a < b) {a = b; return true;}
return false;
}
template <class T1, class T2>
bool minimize(T1 &a, T2 b){
if (a > b) {a = b; return true;}
return false;
}
template <class T>
void printArr(T container, string separator = " ", string finish = "\n", ostream &out = cout){
for(auto item: container) out << item << separator;
out << finish;
}
const int MAX_N = 65;
const int MOD = (int)1e9 + 7;
void add(int &x, int y) {
x += y;
if (x >= MOD) x -= MOD;
}
void sub(int &x, int y) {
x -= y;
if (x < 0) x += MOD;
}
int nNode, nPair, k;
vector<ii> adj[MAX_N];
ii magics[MAX_N];
int poww[MAX_N];
vector<int> path[MAX_N];
bool dfs(int u, int p, int dest, int id) {
bool ok = (u == dest);
for (ii e : adj[u]) {
int v = e.F, edgeID = e.S;
if (v == p) continue;
if (dfs(v, u, dest, id)) {
path[id].push_back(edgeID);
ok = true;
}
}
return ok;
}
int par[MAX_N], sz[MAX_N];
int nCom;
int getP(int a) {
return (a == par[a] ? a : par[a] = getP(par[a]));
}
void unite(int u, int v) {
u = getP(u), v = getP(v);
if (u == v) return;
nCom--;
if (sz[u] < sz[v]) swap(u, v);
par[v] = u;
sz[u] += sz[v];
}
int calc(int mask) {
FOR(i, 1, nNode - 1) par[i] = i, sz[i] = 1;
nCom = nNode - 1;
FOR(i, 0, nPair - 1) if (mask >> i & 1) {
FOR(j, 0, (int)path[i + 1].size() - 2)
unite(path[i + 1][j], path[i + 1][j + 1]);
}
return poww[nCom];
}
void solve() {
cin >> nNode >> nPair >> k;
FOR(i, 1, nNode - 1) {
int u, v;
cin >> u >> v;
adj[u].push_back({v, i});
adj[v].push_back({u, i});
}
FOR(i, 1, nPair) {
cin >> magics[i].F >> magics[i].S;
dfs(magics[i].F, -1, magics[i].S, i);
}
poww[0] = 1;
FOR(i, 1, nNode) poww[i] = 1LL * poww[i - 1] * k % MOD;
int ans = 0;
FOR(mask, 0, (1 << nPair) - 1) {
if (__builtin_popcount(mask) & 1)
sub(ans, calc(mask));
else
add(ans, calc(mask));
}
cout << ans;
}
int32_t main() {
if (fopen(task".inp", "r")) {
freopen(task".inp", "r", stdin);
freopen(task".out", "w", stdout);
}
ios_base::sync_with_stdio(0);
cin.tie(0); cout.tie(0);
bool multitest = 0;
int numTest = 1;
if (multitest) cin >> numTest;
while (numTest--) {
solve();
}
return 0;
}
/* Lak lu theo dieu nhac!!!! */
컴파일 시 표준 에러 (stderr) 메시지
Main.cpp: In function 'int32_t main()':
Main.cpp:119:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
119 | freopen(task".inp", "r", stdin);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
Main.cpp:120:16: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
120 | freopen(task".out", "w", stdout);
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
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