#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const ll MOD = 1000000007;
struct Matrix{
int n, m;
ll mat[2][2];
Matrix(){}
Matrix(int n, int m): n(n), m(m){
for(int i=0; i<n; i++) for(int j=0; j<m; j++) mat[i][j] = 0;
}
Matrix operator*(const Matrix &r)const{
assert(m == r.n);
Matrix ret (n, r.m);
for(int i=0; i<n; i++){
for(int j=0; j<m; j++){
for(int k=0; k<r.m; k++){
ret.mat[i][k] += mat[i][j] * r.mat[j][k];
ret.mat[i][k] %= MOD;
}
}
}
return ret;
}
};
ll mpow(ll x, ll y){
if(!y) return 1;
if(y%2) return mpow(x, y-1) * x % MOD;
ll tmp = mpow(x, y/2);
return tmp*tmp%MOD;
}
Matrix BasicMatrix(int n, int m){
Matrix mat (n, m);
assert(n==m);
for(int i=0; i<n; i++) mat.mat[i][i] = 1;
return mat;
}
Matrix mpow(Matrix x, ll y){
if(!y) return BasicMatrix(x.n, x.m);
if(y&1) return mpow(x, y-1) * x;
Matrix tmp = mpow(x, y/2);
return tmp * tmp;
}
ll n;
ll k;
vector<int> link[1002];
ll mat[1002][1002];
ll depth[1002];
ll group[1002], groupCnt[2];
ll ans;
ll DP[2][1002];
ll find1[1002];
void groupDfs(int x, int p=-1){
groupCnt[group[x]]++;
for(auto y: link[x]){
if(y==p) continue;
group[y] = !group[x];
groupDfs(y, x);
}
}
void dfs(int x, int p, int r){
for(auto y: link[x]){
if(y==p) continue;
depth[y] = depth[x] + 1;
dfs(y, x, r);
if(!mat[r][y]) mat[r][x] = 1;
}
}
int dfsFind(int x, int p, int dp, int r){ /// 무조건 지나야 하는 상대 차례 점 개수 찾기
if(dp % 2 == 0){ /// my turn
int cnt = 0;
for(auto y: link[x]){
// if(mat[r][y] != mat[x][y]){
// printf("%d %d %d\n", y, x, r);
// }
assert(mat[r][y] == mat[x][y]);
if(y!=p && !mat[x][y]) cnt++;
}
if(cnt > 1) return 0;
assert(cnt == 1);
for(auto y: link[x]){
if(y!=p && !mat[x][y]) return dfsFind(y, x, dp+1, r);
}
exit(1);
}
else{ /// your turn
int ret = 1;
for(auto y: link[x]){
if(y==p) continue;
ret += dfsFind(y, x, dp+1, r);
}
return ret;
}
}
int main(){
scanf("%lld %lld", &n, &k);
for(int i=1; i<n; i++){
int x, y;
scanf("%d %d", &x, &y);
link[x].push_back(y);
link[y].push_back(x);
}
groupDfs(1);
for(int i=1; i<=n; i++){
dfs(i, -1, i);
}
for(int i=1; i<=n; i++){
if(mat[i][i]) find1[i] = groupCnt[!group[i]] - dfsFind(i, -1, 0, i);
else find1[i] = dfsFind(i, -1, 1, i);
DP[0][i] = mat[i][i];
}
Matrix first (1, 2);
first.mat[0][0] = first.mat[0][1] = 0;
for(int i=1; i<=n; i++){
if(mat[i][i]) first.mat[0][0]++;
else first.mat[0][1]++;
}
Matrix multiplier (2, 2); /// 0: WIN, 1: LOSE
for(int i=1; i<=n; i++){
if(mat[i][i]){
multiplier.mat[0][0] = (multiplier.mat[0][0] + n) % MOD;
multiplier.mat[1][0] = (multiplier.mat[1][0] + groupCnt[group[i]]) % MOD;
multiplier.mat[1][0] = (multiplier.mat[1][0] + find1[i]) % MOD;
multiplier.mat[1][1] = (multiplier.mat[1][1] + n - groupCnt[group[i]] - find1[i] + MOD)%MOD;
}
else{
multiplier.mat[1][0] = (multiplier.mat[1][0] + find1[i]) % MOD;
multiplier.mat[0][1] = (multiplier.mat[0][1] + n) % MOD;
multiplier.mat[1][1] = (multiplier.mat[1][1] + n - find1[i]) % MOD;
}
}
multiplier = mpow(multiplier, k-1);
first = first * multiplier;
ll Wsum = first.mat[0][0], Lsum = first.mat[0][1];
ll ans = 0;
if(mat[1][1]){
ans = (Wsum * n + groupCnt[group[1]] * Lsum + find1[1] * Lsum) % MOD;
}
else ans = find1[1] * Lsum % MOD;
printf("%lld", ans);
}
Compilation message
startrek.cpp: In function 'int main()':
startrek.cpp:109:10: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
109 | scanf("%lld %lld", &n, &k);
| ~~~~~^~~~~~~~~~~~~~~~~~~~~
startrek.cpp:112:14: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
112 | scanf("%d %d", &x, &y);
| ~~~~~^~~~~~~~~~~~~~~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 KB |
Output is correct |
| 2 |
Runtime error |
23 ms |
16404 KB |
Execution killed with signal 6 |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 KB |
Output is correct |
| 2 |
Correct |
0 ms |
340 KB |
Output is correct |
| 3 |
Correct |
0 ms |
340 KB |
Output is correct |
| 4 |
Correct |
0 ms |
340 KB |
Output is correct |
| 5 |
Correct |
0 ms |
340 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 KB |
Output is correct |
| 2 |
Runtime error |
2 ms |
1492 KB |
Execution killed with signal 6 |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 KB |
Output is correct |
| 2 |
Runtime error |
2 ms |
1492 KB |
Execution killed with signal 6 |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 KB |
Output is correct |
| 2 |
Runtime error |
2 ms |
1492 KB |
Execution killed with signal 6 |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 KB |
Output is correct |
| 2 |
Runtime error |
2 ms |
1492 KB |
Execution killed with signal 6 |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 KB |
Output is correct |
| 2 |
Runtime error |
2 ms |
1492 KB |
Execution killed with signal 6 |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
340 KB |
Output is correct |
| 2 |
Runtime error |
23 ms |
16404 KB |
Execution killed with signal 6 |
| 3 |
Halted |
0 ms |
0 KB |
- |
