#include <iostream>
#include <vector>
#include <queue>
#include <algorithm>
#include <set>
#include <stack>
#include <limits.h>
#include <math.h>
#include <iomanip>
#include <bitset>
#include <unordered_map>
#include <unordered_set>
#include <map>
#include <cstring>
#include <sstream>
#pragma GCC target("popcnt")
typedef long long ll;
typedef long double ld;
using namespace std;
const int MOD=1e9+7;
typedef pair<ll,ll>point;
//#define x first
//#define y second
ll powm(ll base,ll ex){
base%=MOD;
ex%=MOD-1;
ll res=1;
for(int p=0;p<64;p++){
if(ex&(1LL<<p))
res*=base;
res%=MOD;
base*=base;
base%=MOD;
}
return res;
}
ll inv(ll n){
return powm(n,MOD-2);
}
ll n;
ll d;
vector<int> nodes[100000];
int parents[100000];
int to(int a,int b){
if(a==b)
return a+200000;
if(parents[a]==b)
return a;
return b+100000;
}
void init_parents(int node,int par){
parents[node]=par;
for(int ne:nodes[node]){
if(ne==par)
continue;
init_parents(ne,node);
}
}
bool dpt1[300000];
bool dp1[300000];
bool winning(int node,int par);
bool dpt3[100000];
int dp3[100000];
int get1(int node){
if(dpt3[node])
return dp3[node];
int num=0;
for(int ne:nodes[node]){
if(ne==parents[node])
continue;
num+=!winning(ne,node);
}
dpt3[node]=true;
dp3[node]=num;
return num;
}
bool winning(int node,int par){
int t=to(node,par);
if(dpt1[t])
return dp1[t];
int num=get1(node);
if(par!=parents[node]){
if(node!=0)
num+=!winning(parents[node],node);
if(node!=par)
num-=!winning(par,node);
}
bool res=num>0;
dpt1[t]=true;
dp1[t]=res;
return res;
}
bool dpt2[300000];
int dp2[300000];
int count_critical(int node,int par);
bool dpt4[300000];
pair<int,pair<int,int>> dp4[300000];
pair<int,pair<int,int>> get2(int node){
if(dpt4[node])
return dp4[node];
int l_count=0;
int l_ch1=-1;
int l_ch2=-1;
for(int ne:nodes[node]){
if(!winning(ne,node)){
l_count++;
if(l_ch1==-1)
l_ch1=ne;
else
l_ch2=ne;
}
}
dpt4[node]=false;
dp4[node]={l_count,{l_ch1,l_ch2}};
return{l_count,{l_ch1,l_ch2}};
}
bool dpt5[300000];
int dp5[300000];
int get3(int node){
if(dpt5[node])
return dp5[node];
int res=1;
for(int ne:nodes[node]){
if(ne==parents[node])
continue;
res+=count_critical(ne,node);
}
dpt5[node]=true;
dp5[node]=res;
return res;
}
int count_critical(int node,int par){
int t=to(node,par);
if(dpt2[t])
return dp2[t];
int r=0;
if(winning(node,par)){
auto res=get2(node);
int l_count=res.first;
int l_ch1=res.second.first;
int l_ch2=res.second.second;
if(l_ch2==par)
l_count--;
if(l_ch1==par){
l_count--;
l_ch1=l_ch2;
}
if(l_count!=1)
return 0;
r=count_critical(l_ch1,node);
}else{
r=get3(node);
if(par!=parents[node]){
if(node!=0)
r+=count_critical(parents[node],node);
if(node!=par)
r-=count_critical(par,node);
}
}
dpt2[t]=true;
dp2[t]=r;
return r;
}
int main(){
ios::sync_with_stdio(false);
cout.tie(NULL);
cin.tie(NULL);
//freopen("speeding.in","r",stdin);
//freopen("speeding.out","w",stdout);
cin>>n>>d;
for(int i=1;i<n;i++){
int a,b;
cin>>a>>b;
a--;b--;
nodes[a].push_back(b);
nodes[b].push_back(a);
}
init_parents(0,0);
ll num_l=0;
for(int i=0;i<n;i++)
num_l+=!winning(i,i);
ll E=0;
for(int i=0;i<n;i++){
ll res=count_critical(i,i);
if(winning(i,i))
E+=res;
else
E+=MOD-res;
E%=MOD;
}
ll L=1;
L*=powm(n,2*d)+MOD-powm(E,d);
L%=MOD;
L*=inv(n*n+MOD-E);
L%=MOD;
L*=num_l;
L%=MOD;
ll all_combs=powm(n,2*d);
ll res=L*count_critical(0,0);
res%=MOD;
if(winning(0,0))
res=all_combs+MOD-res;
res%=MOD;
cout<<res<<"\n";
return 0;
}
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
2644 KB |
Output is correct |
2 |
Correct |
2 ms |
2772 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
2644 KB |
Output is correct |
2 |
Correct |
1 ms |
2644 KB |
Output is correct |
3 |
Correct |
1 ms |
2644 KB |
Output is correct |
4 |
Correct |
2 ms |
2680 KB |
Output is correct |
5 |
Correct |
2 ms |
2644 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
2680 KB |
Output is correct |
2 |
Correct |
2 ms |
2644 KB |
Output is correct |
3 |
Correct |
2 ms |
2772 KB |
Output is correct |
4 |
Correct |
1 ms |
2644 KB |
Output is correct |
5 |
Correct |
2 ms |
2772 KB |
Output is correct |
6 |
Correct |
3 ms |
2680 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
2680 KB |
Output is correct |
2 |
Correct |
2 ms |
2644 KB |
Output is correct |
3 |
Correct |
2 ms |
2772 KB |
Output is correct |
4 |
Correct |
1 ms |
2644 KB |
Output is correct |
5 |
Correct |
2 ms |
2772 KB |
Output is correct |
6 |
Correct |
3 ms |
2680 KB |
Output is correct |
7 |
Correct |
2 ms |
2900 KB |
Output is correct |
8 |
Correct |
2 ms |
2900 KB |
Output is correct |
9 |
Correct |
2 ms |
2772 KB |
Output is correct |
10 |
Correct |
2 ms |
2772 KB |
Output is correct |
11 |
Correct |
2 ms |
2772 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
2680 KB |
Output is correct |
2 |
Correct |
2 ms |
2644 KB |
Output is correct |
3 |
Correct |
2 ms |
2772 KB |
Output is correct |
4 |
Correct |
1 ms |
2644 KB |
Output is correct |
5 |
Correct |
2 ms |
2772 KB |
Output is correct |
6 |
Correct |
3 ms |
2680 KB |
Output is correct |
7 |
Correct |
2 ms |
2900 KB |
Output is correct |
8 |
Correct |
2 ms |
2900 KB |
Output is correct |
9 |
Correct |
2 ms |
2772 KB |
Output is correct |
10 |
Correct |
2 ms |
2772 KB |
Output is correct |
11 |
Correct |
2 ms |
2772 KB |
Output is correct |
12 |
Correct |
58 ms |
16592 KB |
Output is correct |
13 |
Correct |
75 ms |
22512 KB |
Output is correct |
14 |
Correct |
39 ms |
11592 KB |
Output is correct |
15 |
Correct |
56 ms |
11624 KB |
Output is correct |
16 |
Correct |
69 ms |
11664 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
2680 KB |
Output is correct |
2 |
Correct |
2 ms |
2644 KB |
Output is correct |
3 |
Correct |
2 ms |
2772 KB |
Output is correct |
4 |
Correct |
1 ms |
2644 KB |
Output is correct |
5 |
Correct |
2 ms |
2772 KB |
Output is correct |
6 |
Correct |
3 ms |
2680 KB |
Output is correct |
7 |
Correct |
2 ms |
2900 KB |
Output is correct |
8 |
Correct |
2 ms |
2900 KB |
Output is correct |
9 |
Correct |
2 ms |
2772 KB |
Output is correct |
10 |
Correct |
2 ms |
2772 KB |
Output is correct |
11 |
Correct |
2 ms |
2772 KB |
Output is correct |
12 |
Correct |
1 ms |
2676 KB |
Output is correct |
13 |
Correct |
2 ms |
2816 KB |
Output is correct |
14 |
Correct |
1 ms |
2644 KB |
Output is correct |
15 |
Correct |
2 ms |
2680 KB |
Output is correct |
16 |
Correct |
1 ms |
2676 KB |
Output is correct |
17 |
Correct |
1 ms |
2680 KB |
Output is correct |
18 |
Correct |
1 ms |
2772 KB |
Output is correct |
19 |
Correct |
1 ms |
2680 KB |
Output is correct |
20 |
Correct |
1 ms |
2644 KB |
Output is correct |
21 |
Correct |
2 ms |
2900 KB |
Output is correct |
22 |
Correct |
2 ms |
2900 KB |
Output is correct |
23 |
Correct |
2 ms |
2772 KB |
Output is correct |
24 |
Correct |
2 ms |
2772 KB |
Output is correct |
25 |
Correct |
2 ms |
2772 KB |
Output is correct |
26 |
Correct |
2 ms |
2772 KB |
Output is correct |
27 |
Correct |
2 ms |
2900 KB |
Output is correct |
28 |
Correct |
2 ms |
2812 KB |
Output is correct |
29 |
Correct |
2 ms |
2812 KB |
Output is correct |
30 |
Correct |
2 ms |
2772 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
2680 KB |
Output is correct |
2 |
Correct |
2 ms |
2644 KB |
Output is correct |
3 |
Correct |
2 ms |
2772 KB |
Output is correct |
4 |
Correct |
1 ms |
2644 KB |
Output is correct |
5 |
Correct |
2 ms |
2772 KB |
Output is correct |
6 |
Correct |
3 ms |
2680 KB |
Output is correct |
7 |
Correct |
2 ms |
2900 KB |
Output is correct |
8 |
Correct |
2 ms |
2900 KB |
Output is correct |
9 |
Correct |
2 ms |
2772 KB |
Output is correct |
10 |
Correct |
2 ms |
2772 KB |
Output is correct |
11 |
Correct |
2 ms |
2772 KB |
Output is correct |
12 |
Correct |
58 ms |
16592 KB |
Output is correct |
13 |
Correct |
75 ms |
22512 KB |
Output is correct |
14 |
Correct |
39 ms |
11592 KB |
Output is correct |
15 |
Correct |
56 ms |
11624 KB |
Output is correct |
16 |
Correct |
69 ms |
11664 KB |
Output is correct |
17 |
Correct |
1 ms |
2676 KB |
Output is correct |
18 |
Correct |
2 ms |
2816 KB |
Output is correct |
19 |
Correct |
1 ms |
2644 KB |
Output is correct |
20 |
Correct |
2 ms |
2680 KB |
Output is correct |
21 |
Correct |
1 ms |
2676 KB |
Output is correct |
22 |
Correct |
1 ms |
2680 KB |
Output is correct |
23 |
Correct |
1 ms |
2772 KB |
Output is correct |
24 |
Correct |
1 ms |
2680 KB |
Output is correct |
25 |
Correct |
1 ms |
2644 KB |
Output is correct |
26 |
Correct |
2 ms |
2900 KB |
Output is correct |
27 |
Correct |
2 ms |
2900 KB |
Output is correct |
28 |
Correct |
2 ms |
2772 KB |
Output is correct |
29 |
Correct |
2 ms |
2772 KB |
Output is correct |
30 |
Correct |
2 ms |
2772 KB |
Output is correct |
31 |
Correct |
2 ms |
2772 KB |
Output is correct |
32 |
Correct |
2 ms |
2900 KB |
Output is correct |
33 |
Correct |
2 ms |
2812 KB |
Output is correct |
34 |
Correct |
2 ms |
2812 KB |
Output is correct |
35 |
Correct |
2 ms |
2772 KB |
Output is correct |
36 |
Correct |
67 ms |
16644 KB |
Output is correct |
37 |
Correct |
65 ms |
22496 KB |
Output is correct |
38 |
Correct |
38 ms |
11656 KB |
Output is correct |
39 |
Correct |
59 ms |
11596 KB |
Output is correct |
40 |
Correct |
50 ms |
11644 KB |
Output is correct |
41 |
Correct |
60 ms |
19692 KB |
Output is correct |
42 |
Correct |
58 ms |
20892 KB |
Output is correct |
43 |
Correct |
34 ms |
10604 KB |
Output is correct |
44 |
Correct |
54 ms |
11628 KB |
Output is correct |
45 |
Correct |
50 ms |
11616 KB |
Output is correct |
# |
결과 |
실행 시간 |
메모리 |
Grader output |
1 |
Correct |
1 ms |
2644 KB |
Output is correct |
2 |
Correct |
2 ms |
2772 KB |
Output is correct |
3 |
Correct |
1 ms |
2644 KB |
Output is correct |
4 |
Correct |
1 ms |
2644 KB |
Output is correct |
5 |
Correct |
1 ms |
2644 KB |
Output is correct |
6 |
Correct |
2 ms |
2680 KB |
Output is correct |
7 |
Correct |
2 ms |
2644 KB |
Output is correct |
8 |
Correct |
1 ms |
2680 KB |
Output is correct |
9 |
Correct |
2 ms |
2644 KB |
Output is correct |
10 |
Correct |
2 ms |
2772 KB |
Output is correct |
11 |
Correct |
1 ms |
2644 KB |
Output is correct |
12 |
Correct |
2 ms |
2772 KB |
Output is correct |
13 |
Correct |
3 ms |
2680 KB |
Output is correct |
14 |
Correct |
2 ms |
2900 KB |
Output is correct |
15 |
Correct |
2 ms |
2900 KB |
Output is correct |
16 |
Correct |
2 ms |
2772 KB |
Output is correct |
17 |
Correct |
2 ms |
2772 KB |
Output is correct |
18 |
Correct |
2 ms |
2772 KB |
Output is correct |
19 |
Correct |
58 ms |
16592 KB |
Output is correct |
20 |
Correct |
75 ms |
22512 KB |
Output is correct |
21 |
Correct |
39 ms |
11592 KB |
Output is correct |
22 |
Correct |
56 ms |
11624 KB |
Output is correct |
23 |
Correct |
69 ms |
11664 KB |
Output is correct |
24 |
Correct |
1 ms |
2676 KB |
Output is correct |
25 |
Correct |
2 ms |
2816 KB |
Output is correct |
26 |
Correct |
1 ms |
2644 KB |
Output is correct |
27 |
Correct |
2 ms |
2680 KB |
Output is correct |
28 |
Correct |
1 ms |
2676 KB |
Output is correct |
29 |
Correct |
1 ms |
2680 KB |
Output is correct |
30 |
Correct |
1 ms |
2772 KB |
Output is correct |
31 |
Correct |
1 ms |
2680 KB |
Output is correct |
32 |
Correct |
1 ms |
2644 KB |
Output is correct |
33 |
Correct |
2 ms |
2900 KB |
Output is correct |
34 |
Correct |
2 ms |
2900 KB |
Output is correct |
35 |
Correct |
2 ms |
2772 KB |
Output is correct |
36 |
Correct |
2 ms |
2772 KB |
Output is correct |
37 |
Correct |
2 ms |
2772 KB |
Output is correct |
38 |
Correct |
2 ms |
2772 KB |
Output is correct |
39 |
Correct |
2 ms |
2900 KB |
Output is correct |
40 |
Correct |
2 ms |
2812 KB |
Output is correct |
41 |
Correct |
2 ms |
2812 KB |
Output is correct |
42 |
Correct |
2 ms |
2772 KB |
Output is correct |
43 |
Correct |
67 ms |
16644 KB |
Output is correct |
44 |
Correct |
65 ms |
22496 KB |
Output is correct |
45 |
Correct |
38 ms |
11656 KB |
Output is correct |
46 |
Correct |
59 ms |
11596 KB |
Output is correct |
47 |
Correct |
50 ms |
11644 KB |
Output is correct |
48 |
Correct |
60 ms |
19692 KB |
Output is correct |
49 |
Correct |
58 ms |
20892 KB |
Output is correct |
50 |
Correct |
34 ms |
10604 KB |
Output is correct |
51 |
Correct |
54 ms |
11628 KB |
Output is correct |
52 |
Correct |
50 ms |
11616 KB |
Output is correct |
53 |
Correct |
75 ms |
22576 KB |
Output is correct |
54 |
Correct |
74 ms |
20316 KB |
Output is correct |
55 |
Correct |
42 ms |
9936 KB |
Output is correct |
56 |
Correct |
55 ms |
16608 KB |
Output is correct |
57 |
Correct |
52 ms |
11824 KB |
Output is correct |
58 |
Correct |
53 ms |
11736 KB |
Output is correct |
59 |
Correct |
58 ms |
11716 KB |
Output is correct |
60 |
Correct |
57 ms |
11608 KB |
Output is correct |