#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define int ll
typedef pair<int,int> pi;
typedef vector <int> vi;
typedef vector <pi> vpi;
typedef pair<pi, ll> pii;
typedef set <ll> si;
typedef long double ld;
#define f first
#define s second
#define mp make_pair
#define FOR(i,s,e) for(int i=s;i<=int(e);++i)
#define DEC(i,s,e) for(int i=s;i>=int(e);--i)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define lbd(x, y) lower_bound(all(x), y)
#define ubd(x, y) upper_bound(all(x), y)
#define aFOR(i,x) for (auto i: x)
#define mem(x,i) memset(x,i,sizeof x)
#define fast ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0)
#define maxn 400010
#define INF (ll)(1e9+10)
#define MOD 1000000007
typedef pair <vi, int> pvi;
typedef pair <int,pi> ipi;
typedef vector <pii> vpii;
typedef pair <pi,pi> pipi;
int N,D,a,b;
vi adj[maxn];
bool win[maxn];
int firstpar[maxn], depth[maxn];
void dfs(int x, int p){
win[x] = 0;
aFOR(i,adj[x]) if (i != p){
depth[i] = depth[x] + 1; dfs(i,x);
win[x] |= !win[i];
}
}
void dfs2(int x,int p){
if (p == -1) firstpar[x] = x;
else{
firstpar[x] = firstpar[p];
aFOR(i, adj[p]) if (depth[i] == depth[x] && i != x && !win[i]){
firstpar[x] = x;
}
}
aFOR(i,adj[x]) if (i != p) dfs2(i,x);
}
int qexp(int a,int b){
int ans = 1;
while (b){
//~ cout << a << ' ' << b << ' ' << ans << '\n';
if (b & 1) (ans *= a) %= MOD;
(a *= a) %= MOD;
b >>= 1;
}
return ans;
}
int32_t main(){
fast;
cin >> N >> D;
FOR(i,1,N-1){
cin >> a >> b; adj[a].pb(b); adj[b].pb(a);
}
//~ cout << qexp(N, 2 * D);
//~ return 0;
int numnexte = 0,numnexto = 0, numwin = 0;
int ans = 0;
int nnexte1 = 0, nnexto1 = 0, nwin1 = 0;
FOR(i,1,N){
depth[i] = 0; dfs(i,-1); dfs2(i,-1);
ans += win[i];
int nnexte = 0,nnexto = 0, nwin = 0;
FOR(j,1,N){
if (win[j]){
nwin++;
if (j == 1) nwin1++;
}else if (firstpar[j] == i){
if (depth[j] % 2 == 0){
nnexte++; if (j == 1) nnexte1++;
}else{
nnexto++; if (j == 1) nnexto1++;
}
}else if ((depth[j] - depth[firstpar[j]]) % 2 == 1){
nwin++; if (j == 1) nwin1++;
}
}
numnexte += nnexte; numnexto += nnexto; numwin += nwin;
}
//~ cout << ans << ' ' << numnexto << ' ' << numnexte << ' ' << numwin << '\n';
//~ DEC(j,D-1,1){
//~ (ans *= (numnexto - numnexte)) %= MOD;
//~ (ans += (qexp(N, 2*(D-j)-1) * (numnexte + numwin)) % MOD) %= MOD;
//~ cout << ans << '\n';
//~ }
int m = numnexto - numnexte, c = numwin + numnexte;
int r = (m * qexp((N*N)%MOD, MOD - 2)) % MOD; //mN^-2
ans = (qexp(m, D - 1) * ans) % MOD;
int geomseries = ((qexp(r, D - 1) - 1) * qexp(r - 1, MOD - 2)) % MOD;
ans += (((geomseries * qexp(N, 2*(D-1)-1)) % MOD) * c) % MOD;
(ans += MOD) %= MOD;
ans = (((nnexto1 - nnexte1) * ans) % MOD + (qexp(N, 2*D-1)* (nwin1 + nnexte1)) % MOD) % MOD;
cout << (ans + MOD) % MOD;
//~ int x = ans; ans = 0;
//~ FOR(i,1,N){
//~ depth[i] = 0; dfs(i,-1); dfs2(i,-1);
//~ if (win[1]) (ans += N) %= MOD;
//~ else if (firstpar[1] == i){
//~ if (depth[1] % 2 == 0) (ans += N - x) %= MOD;
//~ else (ans += x) %= MOD;
//~ }else if ((depth[1] - depth[firstpar[1]]) % 2 == 1) (ans += N) %= MOD;
//~ }
//~ cout << ans;
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1082 ms |
9684 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
7 ms |
9684 KB |
Output is correct |
| 2 |
Correct |
6 ms |
9728 KB |
Output is correct |
| 3 |
Correct |
5 ms |
9684 KB |
Output is correct |
| 4 |
Correct |
5 ms |
9720 KB |
Output is correct |
| 5 |
Correct |
5 ms |
9720 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1095 ms |
9684 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1095 ms |
9684 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1095 ms |
9684 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1095 ms |
9684 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1095 ms |
9684 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Execution timed out |
1082 ms |
9684 KB |
Time limit exceeded |
| 2 |
Halted |
0 ms |
0 KB |
- |
