#include<bits/stdc++.h>
//#include<iostream>
//#include<vector>
using namespace std;
#define int long long
const int mod=1e9+7;
struct matrix{
int a=1;
int b=0;
int c=0;
int d=1;
};
matrix zero={1, 0, 0, 1};
vector<int> mul(matrix a, vector<int> b){
vector<int> ans(2, -1);
ans[0]=(a.a*b[0])%mod +(a.b*b[1])%mod;
ans[0]%=mod;
ans[1]=(a.c*b[0])%mod +(a.d*b[1])%mod;
ans[1]%=mod;
return ans;
}
matrix multiply(matrix a, matrix b){
matrix ans;
ans.a=(a.a*b.a)%mod + (a.b*b.c)%mod;
ans.a%=mod;
ans.b=(a.a*b.b)%mod + (a.b*b.d)%mod;
ans.b%=mod;
ans.c=(a.c*b.a)%mod + (a.d*b.c)%mod;
ans.c%=mod;
ans.d=(a.c*b.b)%mod + (a.d*b.d)%mod;
ans.d%=mod;
return ans;
}
matrix power(matrix a, int e){
if(e==0){
return zero;
}
matrix res=power(a, e/2);
res=multiply(res, res);
if(e%2==1){
res=multiply(res, a);
}
return res;
}
// vertex_status ist:
bool dfs_win(int v, int p, vector<vector<int> >& adi, vector<int>& vertex_status, vector<vector<int>>& red_neighbors){
if (vertex_status[v] == -2) {
vertex_status[v] = p;
for(auto u: adi[v]){
if(u==p) continue;
if(!dfs_win(u, v, adi, vertex_status, red_neighbors)){
red_neighbors[v].push_back(u);
}
}
} else {
if (vertex_status[v] >= 0 && vertex_status[v] != p) {
auto u = vertex_status[v];
if(!dfs_win(u, v, adi, vertex_status, red_neighbors)){
red_neighbors[v].push_back(u);
}
vertex_status[v] = -1;
}
}
if (vertex_status[v] == p) {
return red_neighbors[v].size() > 0;
} else {
if (red_neighbors[v].size() >= 2) return true;
if (red_neighbors[v].size() == 0) return false;
return red_neighbors[v][0] != p;
}
}
int dfs_redforce(int v, int p, vector<vector<int> >& adi, vector<vector<int>>& red_neighbors, vector<int>& vertex_status, vector<unordered_map<int, int> >& redf, vector<int>& summe){
if(vertex_status[v]==-2){
int redforce=0;
bool is_green;
if (red_neighbors[v].size() >= 2) is_green = true;
else if (red_neighbors[v].size() == 0) is_green = false;
else is_green = red_neighbors[v][0] != p;
for(auto u: adi[v]){
if(u==p) continue;
redf[v][u]=dfs_redforce(u, v, adi, red_neighbors, vertex_status, redf, summe);
summe[v]+=redf[v][u];
}
if(!is_green){ //red
redforce++;
redforce+=summe[v];
}
else { //green with one red child
vector<int> red_children;
for (int x : red_neighbors[v]) if (x != p) red_children.push_back(x);
if (red_children.size() == 1) {
redforce+=redf[v][red_children[0]];
}
}
vertex_status[v]=p;
return redforce;
}
else{
int redforce=0;
bool is_green;
if (red_neighbors[v].size() >= 2) is_green = true;
else if (red_neighbors[v].size() == 0) is_green = false;
else is_green = red_neighbors[v][0] != p;
if(!is_green){ //red
redforce++;
if(vertex_status[v]!=p){
redf[v][vertex_status[v]]=dfs_redforce(vertex_status[v], v, adi, red_neighbors, vertex_status, redf, summe);
summe[v]+=vertex_status[v];
}
redforce+=summe[v];
redforce-=redf[v][p];
}
else { //green with one red child
bool needed=red_neighbors[v].size()<3;
int u=red_neighbors[v][0];
if(red_neighbors[v].size()==2){
if(red_neighbors[v][0]==p) u=red_neighbors[v][1];
else if(red_neighbors[v][1]!=p) needed=false;
}
if (needed) {
if(vertex_status[v]==u){
redf[v][u]=dfs_redforce(u, v, adi, red_neighbors, vertex_status, redf, summe);
summe[v]+=redf[v][u];
vertex_status[v]=-1;
}
redforce+=redf[v][u];
}
redforce-=redf[v][p];
}
return redforce;
}
}
signed main(){
ios_base::sync_with_stdio(false);
cin.tie(0);
//freopen("input1.txt", "r", stdin);
//freopen("out.txt", "w", stdout);
int n, d;
cin >> n >> d;
vector<vector<int> > adi(n);
for(int i=0; i<n-1; i++){
int a,b;
cin >> a >> b;
adi[a-1].push_back(b-1);
adi[b-1].push_back(a-1);
}
int G=0; int R=0;
int g1=0; int r1=0;
int c=0;
vector<int> vertex_status(n, -2);
vector<int> vertex_status2(n, -2);
vector<vector<int>> red_neighbors(n);
vector<unordered_map<int,int> > redf(n);
vector<int> summe(n, 0);
for(int i=n-1; i>=0; i--){
vector<int> redchild(n, -1);
vector<int> cnt_red_children(n, 0);
bool we_win=dfs_win(i, -1, adi, vertex_status, red_neighbors);
int redforce=dfs_redforce(i, -1, adi, red_neighbors, vertex_status2, redf, summe);
if(we_win){
c++;
g1=n;
r1=n-redforce;
}
else{
g1=0;
r1=redforce;
}
G+=g1; G%=mod;
R+=r1; R%=mod;
}
matrix m1={g1, r1, 0, 0};
matrix m2={G, R, ((n*n)-G)%mod, ((n*n)-R)%mod};
matrix p=power(m2, d-1);
vector<int> v=mul(p, {c, n-c});
vector<int> ans=mul(m1, v);
cout << ans[0] << "\n";
}
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
1 ms |
340 KB |
Execution killed with signal 11 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
1 ms |
340 KB |
Execution killed with signal 11 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
1 ms |
448 KB |
Execution killed with signal 11 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
1 ms |
448 KB |
Execution killed with signal 11 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
1 ms |
448 KB |
Execution killed with signal 11 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
1 ms |
448 KB |
Execution killed with signal 11 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
1 ms |
448 KB |
Execution killed with signal 11 |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Runtime error |
1 ms |
340 KB |
Execution killed with signal 11 |
| 2 |
Halted |
0 ms |
0 KB |
- |
