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>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define fi first
#define se second
#define ll long long
#define ld long double
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(), (x).end()
#define pb push_back
#define mpp make_pair
#define ve vector
using namespace std;
using namespace __gnu_pbds;
template<class T> using oset = tree<T,null_type,less<T>,rb_tree_tag,tree_order_statistics_node_update>;
const ll inf = 1e18; const int iinf = 1e9;
typedef pair<ll, ll> pll;
typedef pair<int, int> pii;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
template <typename T> inline bool chmin(T& a, T b) { return (a > b ? a = b, 1 : 0); }
template <typename T> inline bool chmax(T& a, T b) { return (a < b ? a = b, 1 : 0); }
constexpr int md = 1e9 + 7; constexpr int iv2 = (md + 1) / 2;
inline int add(int a, int b) { a += b; if(a>=md){a-=md;} return a; }
inline int sub(int a, int b) { a -= b; if(a<0){a+=md;} return a; }
inline int mul(int a, int b) { return (ll)a * b % md; }
inline int bp(int a, int n) { int res = 1;
for (; n; n >>= 1, a = mul(a, a)) {
if (n & 1) res = mul(res, a);
} return res;
}
inline int inv(int a) { return bp(a, md - 2); }
const int N = 65;
int p[N], rnk[N];
inline void build(int n) { for (int i = 0; i < n; ++i) p[i] = i, rnk[i] = 1; }
inline int par(int v) { if (p[v] == v) { return v; } return (p[v] = par(p[v])); }
inline bool uni(int a, int b) {
a = par(a), b = par(b);
if (a == b) return 0;
if (rnk[a] > rnk[b]) swap(a, b);
p[a] = b, rnk[b] += rnk[a]; return 1;
}
ve<int> gr[N];
int lca[N][N], h[N], ac[N];
inline void dfs(int v, int p) {
for (auto &to : gr[v]) {
if (to == p) continue;
ac[to] = v, h[to] = h[v] + 1;
dfs(to, v);
}
}
inline void solve() {
int n, m, k;
cin >> n >> m >> k;
for (int i = 1; i < n; ++i) {
int v, u;
cin >> v >> u, --v, --u;
gr[v].pb(u), gr[u].pb(v);
}
ve<pii> a(m);
for (auto &[v, u] : a) cin >> v >> u, --v, --u;
dfs(0, 0);
for (int v = 0; v < n; ++v) {
for (int u = 0; u < n; ++u) {
if (v == u) lca[v][u] = v;
else {
int x = v, y = u;
while (x != y) {
if (h[x] < h[y]) swap(x, y);
x = ac[x];
}
lca[v][u] = x;
}
}
}
// for (int i = 0; i < n; ++i) {
// for (int j = 0; j < n; ++j) {
// cout << i + 1 << " " << j + 1 << " -> " << lca[i][j] + 1 << '\n';
// }
// }
// cout << '\n';
int ans = 0;
// cout << '\n';
for (int ma = 0; ma < (1 << m); ++ma) {
build(n);
for (int i = 0; i < m; ++i) {
if (ma >> i & 1 ^ 1) continue;
int x = a[i].fi, y = a[i].se;
int l = lca[x][y];
if (x != l && y != l) uni(x, y);
while (x != l) {
if (ac[x] != l) uni(x, ac[x]);
x = ac[x];
}
while (y != l) {
if (ac[y] != l) uni(y, ac[y]);
y = ac[y];
}
}
int comp = 0;
for (int i = 1; i < n; ++i) comp += (par(i) == i);
// cout << (bitset<3>(ma)) << " " << comp << '\n';
if (__builtin_popcount(ma) & 1 ^ 1) ans = add(ans, bp(k, comp));
else ans = sub(ans, bp(k, comp));
}
cout << ans;
}
signed main() {
ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
int q = 1; // cin >> q;
while (q--) solve();
cerr << fixed << setprecision(3) << "Time execution: " << (double)clock() / CLOCKS_PER_SEC << endl;
}
Compilation message (stderr)
Main.cpp: In function 'void solve()':
Main.cpp:95:16: warning: suggest parentheses around arithmetic in operand of '^' [-Wparentheses]
95 | if (ma >> i & 1 ^ 1) continue;
| ~~~~~~~~^~~
Main.cpp:114:30: warning: suggest parentheses around arithmetic in operand of '^' [-Wparentheses]
114 | if (__builtin_popcount(ma) & 1 ^ 1) ans = add(ans, bp(k, comp));
| ~~~~~~~~~~~~~~~~~~~~~~~^~~
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