#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair <int, int> pii;
typedef pair <ll, ll> pll;
#define long unsigned long
#define pb push_back
#define mp make_pair
#define all(v) (v).begin(),(v).end()
#define rall(v) (v).rbegin(),(v).rend()
#define lb lower_bound
#define ub upper_bound
#define sz(v) int((v).size())
#define do_not_disturb ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
#define endl '\n'
const int mod = 1e9+7;
ll add(ll a, ll b) {
return ((a + b) % mod + mod) % mod;
}
ll mult(ll a, ll b) {
return ((a * b) % mod + mod) % mod;
}
ll binpow(ll a, ll b) {
ll res = 1;
while (b) {
if (b&1) res = mult(res, a);
a = mult(a, a);
b >>= 1;
}
return res;
}
const int N = 1e5+7;
vector <int> graph[N];
int state[N], state_root[N], losing_children[N], parent[N], life_changing[N];
int losing[N], winning[N];
int dfs(int v, int p) {
parent[v] = p;
int l = 0;
for (auto to : graph[v]) {
if (to == parent[v]) {
continue;
}
l += dfs(to, v);
}
losing_children[v] = l;
state[v] = 1 - (losing_children[v] > 0);
return state[v];
}
void dfs2(int v, int i) {
state_root[v] = state[v];
(state[v] ? losing[i] : winning[i])++;
for (auto to : graph[v]) {
if (to == parent[v]) {
continue;
}
if (state[to] && !state[v] && !state[parent[v]] && losing_children[v] == 1) {
losing_children[v]--;
losing_children[to]++;
state[v] = 1;
state[to] = 0;
dfs2(to, i);
losing_children[v]++;
losing_children[to]--;
state[v] = 0;
state[to] = 1;
}
else {
dfs2(to, i);
}
}
}
void dfs3(int v, int i, bool flag = 1) {
if (state[v] && !state[parent[v]] && losing_children[parent[v]] > 1) {
flag = 0;
}
if (state[v] && flag) {
life_changing[i]++;
}
for (auto to : graph[v]) {
if (to == parent[v]) {
continue;
}
dfs3(to, i, flag);
}
}
void solve() {
int n;
ll D;
cin >> n >> D;
for (int i = 1; i < n; i++) {
int a, b;
cin >> a >> b;
graph[a].pb(b);
graph[b].pb(a);
}
if (n == 2) {
cout << binpow(2, D*2) << endl;
}
else if (D <= 1e5) {
ll all_life_changing = 0;
dfs(1, 1);
dfs2(1, D);
for (int i = 1; i <= n; i++) {
dfs(i, i);
dfs3(i, i);
all_life_changing = add(all_life_changing, (state_root[i] ? 1 : -1) * life_changing[i]);
}
for (int j = D-1; j >= 1; j--) {
losing[j] = add(losing[j], mult(add(mult(n, n), -all_life_changing), losing[j+1]));
winning[j] = add(binpow(n, D-j+2), -losing[j]);
}
if (state_root[1]) {
cout << mult(life_changing[1], losing[1]);
}
else {
cout << add(mult(n, winning[1]), mult(n-life_changing[1], losing[1]));
}
}
}
int main() {
do_not_disturb
int t = 1;
//~ cin >> t;
while (t--) {
solve();
}
return 0;
}
/*
13 1
13 1
1 2
1 3
1 4
1 5
5 6
1 12
12 13
1 7
7 8
8 11
8 9
10 9
*/
Compilation message
startrek.cpp:107:2: error: extended character is not valid in an identifier
107 | }
| ^
startrek.cpp:108:2: error: extended character is not valid in an identifier
108 | if (n == 2) {
| ^
startrek.cpp: In function 'void solve()':
startrek.cpp:107:2: error: '\U000000a0' was not declared in this scope
107 | }
| ^
startrek.cpp:108:2: error: '\U000000a0' was not declared in this scope
108 | if (n == 2) {
| ^
startrek.cpp:111:5: error: 'else' without a previous 'if'
111 | else if (D <= 1e5) {
| ^~~~
