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>
typedef long long ll;
using namespace std;
const ll MOD = 1e9 + 7;
vector<int> graph[100001];
ll win_as_root[100001], critical[100001];
void dfs1(int node = 1, int parent = 0) {
for (int i : graph[node]) if (i != parent) {
dfs1(i, node);
win_as_root[node] += (win_as_root[i] == 0);
}
if (!win_as_root[node]) critical[node] = 1;
for (int i : graph[node]) if (i != parent) {
if ((win_as_root[node] == 1 && !win_as_root[i]) || !win_as_root[node])
critical[node] += critical[i];
}
}
void dfs2(int node = 1, int parent = 0, bool par_win = true, ll par_crit = 0) {
win_as_root[node] += !par_win;
ll all_crit = 0, lose_crit = 0;
critical[node] = (win_as_root[node] == 0);
all_crit += par_crit;
if (!par_win) all_crit += par_crit;
if ((win_as_root[node] == 1 && !par_win) || !win_as_root[node])
critical[node] += par_crit;
for (int i : graph[node]) if (i != parent) {
all_crit += critical[i];
if (!win_as_root[i]) lose_crit += critical[i];
if ((win_as_root[node] == 1 && !win_as_root[i]) || !win_as_root[node])
critical[node] += critical[i];
}
for (int i : graph[node]) if (i != parent) {
if (win_as_root[node] - (win_as_root[i] == 0) == 0)
dfs2(i, node, false, all_crit - critical[i] + 1);
else if (win_as_root[node] - (win_as_root[i] == 0) == 1)
dfs2(i, node, true, lose_crit - (win_as_root[i] ? critical[i] : 0));
else
dfs2(i, node, true, 0);
}
}
int main() {
ios_base::sync_with_stdio(0);
cin.tie(0);
ll n, d;
cin >> n >> d;
for (int i = 1; i < n; i++) {
int u, v;
cin >> u >> v;
graph[u].push_back(v);
graph[v].push_back(u);
}
dfs1();
dfs2();
ll lose_cnt = 0;
for (int i = 1; i <= n; i++) lose_cnt += (win_as_root[i] == 0);
if (win_as_root[1])
cout << (n * n - lose_cnt * critical[1]) % MOD;
else
cout << lose_cnt * critical[1] % MOD;
return 0;
}
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