/*************************************
* author: marvinthang *
* created: 03.05.2024 16:12:22 *
*************************************/
#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define left ___left
#define right ___right
#define TIME (1.0 * clock() / CLOCKS_PER_SEC)
#define MASK(i) (1LL << (i))
#define BIT(x, i) ((x) >> (i) & 1)
#define __builtin_popcount __builtin_popcountll
#define ALL(v) (v).begin(), (v).end()
#define REP(i, n) for (int i = 0, _n = (n); i < _n; ++i)
#define REPD(i, n) for (int i = (n); i-- > 0; )
#define FOR(i, a, b) for (int i = (a), _b = (b); i < _b; ++i)
#define FORD(i, b, a) for (int i = (b), _a = (a); --i >= _a; )
#define FORE(i, a, b) for (int i = (a), _b = (b); i <= _b; ++i)
#define FORDE(i, b, a) for (int i = (b), _a = (a); i >= _a; --i)
#define scan_op(...) istream & operator >> (istream &in, __VA_ARGS__ &u)
#define print_op(...) ostream & operator << (ostream &out, const __VA_ARGS__ &u)
#ifdef LOCAL
#include "debug.h"
#else
#define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
#define DB(...) 23
#define db(...) 23
#define debug(...) 23
#endif
template <class U, class V> scan_op(pair <U, V>) { return in >> u.first >> u.second; }
template <class T> scan_op(vector <T>) { for (size_t i = 0; i < u.size(); ++i) in >> u[i]; return in; }
template <class U, class V> print_op(pair <U, V>) { return out << '(' << u.first << ", " << u.second << ')'; }
template <size_t i, class T> ostream & print_tuple_utils(ostream &out, const T &tup) { if constexpr(i == tuple_size<T>::value) return out << ")"; else return print_tuple_utils<i + 1, T>(out << (i ? ", " : "(") << get<i>(tup), tup); }
template <class ...U> print_op(tuple<U...>) { return print_tuple_utils<0, tuple<U...>>(out, u); }
template <class Con, class = decltype(begin(declval<Con>()))> typename enable_if <!is_same<Con, string>::value, ostream&>::type operator << (ostream &out, const Con &con) { out << '{'; for (__typeof(con.begin()) it = con.begin(); it != con.end(); ++it) out << (it == con.begin() ? "" : ", ") << *it; return out << '}'; }
const int MOD = 1e9 + 7;
namespace MODULAR {
inline void fasterLLDivMod(unsigned long long x, unsigned y, unsigned &out_d, unsigned &out_m) {
unsigned xh = (unsigned)(x >> 32), xl = (unsigned)x, d, m;
#ifdef __GNUC__
asm(
"divl %4 \n\t"
: "=a" (d), "=d" (m)
: "d" (xh), "a" (xl), "r" (y)
);
#else
__asm {
mov edx, dword ptr[xh];
mov eax, dword ptr[xl];
div dword ptr[y];
mov dword ptr[d], eax;
mov dword ptr[m], edx;
};
#endif
out_d = d; out_m = m;
}
template <class T> T invGeneral(T a, T b) {
a %= b;
if (!a) return b == 1 ? 0 : -1;
T x = invGeneral(b, a);
return x == -1 ? -1 : ((1 - 1LL * b * x) / a + b) % b;
}
template <int MOD> struct ModInt {
unsigned int val;
ModInt(void): val(0) {}
ModInt(const long long &x) { *this = x; }
ModInt & normalize(const unsigned int &v) {
val = v >= MOD ? v - MOD : v;
return *this;
}
bool operator ! (void) { return !val; }
ModInt & operator = (const ModInt &x) { val = x.val; return *this; }
ModInt & operator = (const long long &x) { return normalize(x % MOD + MOD); }
ModInt operator - (void) { return ModInt(MOD - val); }
ModInt & operator += (const ModInt &other) { return normalize(val + other.val); }
ModInt & operator -= (const ModInt &other) { return normalize(val + MOD - other.val); }
ModInt & operator /= (const ModInt &other) { return *this *= other.inv(); }
ModInt & operator *= (const ModInt &other) {
unsigned dummy;
fasterLLDivMod((unsigned long long) val * other.val, MOD, dummy, val);
return *this;
}
ModInt operator + (const ModInt &other) const { return ModInt(*this) += other; }
ModInt operator - (const ModInt &other) const { return ModInt(*this) -= other; }
ModInt operator * (const ModInt &other) const { return ModInt(*this) *= other; }
ModInt operator / (const ModInt &other) const { return ModInt(*this) /= other; }
ModInt pow(long long n) const {
assert(n >= 0);
ModInt res = 1, a = *this;
for (; n; n >>= 1, a *= a) if (n & 1) res *= a;
return res;
}
ModInt inv(void) const {
int i = invGeneral((int) val, MOD);
assert(~i);
return i;
}
ModInt & operator ++ (void) { return *this += 1; }
ModInt & operator -- (void) { return *this -= 1; }
ModInt operator ++ (int) { ModInt old = *this; operator ++(); return old; }
ModInt operator -- (int) { ModInt old = *this; operator --(); return old; }
friend ModInt operator + (const long long &x, const ModInt &y) { return ModInt(x) + y; }
friend ModInt operator - (const long long &x, const ModInt &y) { return ModInt(x) - y; }
friend ModInt operator * (const long long &x, const ModInt &y) { return ModInt(x) * y; }
friend ModInt operator / (const long long &x, const ModInt &y) { return ModInt(x) / y; }
friend ostream & operator << (ostream &out, const ModInt &x) { return out << x.val; }
friend istream & operator >> (istream &in, ModInt &x) { long long a; in >> a; x = a; return in; }
explicit operator bool(void) const { return val; }
explicit operator int(void) const { return val; }
};
using Modular = ModInt <MOD>;
}
using namespace MODULAR;
template <class T> struct Matrix {
int numRow, numCol; vector <T> val;
// accessors
typename vector<T>::iterator operator [] (int r) { return val.begin() + r * numCol; }
inline T & at(int r, int c) { return val[r * numCol + c]; }
inline T get(int r, int c) const { return val[r * numCol + c]; }
// constructors
Matrix() {}
Matrix(int r, int c): numRow(r), numCol(c), val(r * c) {}
Matrix(const vector <vector <T>> &d) {
numRow = d.size();
numCol = numRow ? d[0].size() : 0;
for (int i = 0; i < numRow; ++i) {
assert((int) d[i].size() == numCol);
copy(d[i].begin(), d[i].end(), back_inserter(val));
}
}
Matrix & set_value(T v) {
for (int i = 0; i < numRow * numCol; ++i) val[i] = v;
return *this;
}
// convert to 2D vector
vector <vector <T>> vecvec(void) const {
vector <vector <T>> res(numRow);
for (int i = 0; i < numRow; ++i)
copy(val.begin() + i * numCol, val.begin() + (i + 1) * numCol, back_inserter(res[i]));
return res;
}
operator vector <vector <T>> () const { return vecvec(); }
static Matrix identity(int n) {
Matrix res(n, n);
for (int i = 0; i < n; ++i) res.at(i, i) = T(1);
return res;
}
friend istream & operator >> (istream &in, Matrix &res) {
for (T &x: res.val) in >> x;
return in;
}
friend ostream & operator << (ostream &out, const Matrix &res) {
for (int i = 0; i < res.numRow * res.numCol; ++i)
cout << res.val[i] << " \n"[i % res.numCol == res.numCol - 1];
return out;
}
Matrix operator - (void) {
Matrix res(numRow, numCol);
for (int i = 0; i < numRow * numCol; ++i) res.val[i] = -val[i];
return res;
}
Matrix operator * (const T &v) {
Matrix res = *this;
for (T &x: res.val) x *= v;
return res;
}
Matrix operator / (const T &v) {
Matrix res = *this;
const T inv = T(1) / v;
for (T &x: res.val) x *= inv;
return res;
}
Matrix operator + (const Matrix &other) const {
int M = numRow, N = numCol;
assert(M == other.numRow); assert(N == other.numCol);
Matrix res = *this;
for (int i = 0; i < numRow * numCol; ++i) res.val[i] += other.val[i];
return res;
}
Matrix operator - (const Matrix &other) const {
int M = numRow, N = numCol;
assert(M == other.numRow); assert(N == other.numCol);
Matrix res = *this;
for (int i = 0; i < numRow * numCol; ++i) res.val[i] -= other.val[i];
return res;
}
Matrix operator * (const Matrix &other) const {
int M = numRow, N = numCol, P = other.numCol;
assert(N == other.numRow);
Matrix t_other = other.transpose();
Matrix res(M, P);
for (int i = 0; i < M; ++i)
for (int j = 0; j < P; ++j)
res.at(i, j) = inner_product(this->val.begin() + N * i, this->val.begin() + N * (i + 1), t_other.val.begin() + t_other.numCol * j, T(0));
return res;
}
Matrix & operator *= (const T &v) { return *this = *this * v; }
Matrix & operator /= (const T &v) { return *this = *this / v; }
Matrix & operator += (const Matrix &other) { return *this = *this + other; }
Matrix & operator -= (const Matrix &other) { return *this = *this - other; }
Matrix & operator *= (const Matrix &other) { return *this = *this * other; }
Matrix pow(long long Exp) const {
int M = numRow;
assert(M == numCol); assert(Exp >= 0);
Matrix res = identity(M);
if (!Exp) return res;
bool is_id = true;
for (int i = 63 - __builtin_clzll(Exp); i >= 0; --i) {
if (!is_id) res *= res;
if (Exp >> i & 1) res *= *this, is_id = false;
}
return res;
}
Matrix transpose(void) const {
Matrix res(numCol, numRow);
for (int i = 0; i < numRow; ++i)
for (int j = 0; j < numCol; ++j)
res.at(j, i) = this->get(i, j);
return res;
}
};
// end of template
void process(void) {
int n; long long d; cin >> n >> d;
vector <vector <int>> adj(n);
REP(i, n - 1) {
int u, v; cin >> u >> v; --u; --v;
adj[u].push_back(v);
adj[v].push_back(u);
}
vector <int> cnt_lose(n), cnt_fw(n), cnt_fl(n), f(n);
auto cal = [&] (int u) {
if (cnt_lose[u] == 1) f[u] = cnt_fl[u];
else if (!cnt_lose[u]) f[u] = cnt_fw[u] + 1;
else f[u] = 0;
};
auto dfs = [&] (auto &&dfs, int u, int par) -> void{
for (int v: adj[u]) if (v != par) {
dfs(dfs, v, u);
cnt_lose[u] += !cnt_lose[v];
(cnt_lose[v] ? cnt_fw[u] : cnt_fl[u]) += f[v];
}
cal(u);
};
dfs(dfs, 0, 0);
vector <int> g(n);
vector <int> lst_win, lst_lose;
auto dfs2 = [&] (auto &&dfs, int u, int par) -> void {
(cnt_lose[u] ? lst_win : lst_lose).push_back(u);
g[u] = f[u];
for (int v: adj[u]) if (v != par) {
cnt_lose[u] -= !cnt_lose[v];
(cnt_lose[v] ? cnt_fw[u] : cnt_fl[u]) -= f[v];
cal(u);
cnt_lose[v] += !cnt_lose[u];
(cnt_lose[u] ? cnt_fw[v] : cnt_fl[v]) += f[u];
cal(v);
dfs(dfs, v, u);
cnt_lose[v] -= !cnt_lose[u];
(cnt_lose[u] ? cnt_fw[v] : cnt_fl[v]) -= f[u];
cal(v);
cnt_lose[u] += !cnt_lose[v];
(cnt_lose[v] ? cnt_fw[u] : cnt_fl[u]) += f[v];
cal(u);
}
};
dfs2(dfs2, 0, 0);
Modular k;
for (int u: lst_win) k += g[u];
for (int u: lst_lose) k -= g[u];
Matrix <Modular> base({{lst_lose.size(), 1LL * n * n}});
Matrix <Modular> trans({
{k, 0},
{1, 1LL * n * n}
});
base *= trans.pow(d - 1);
cout << (cnt_lose[0] ? base[0][1] - g[0] * base[0][0] : g[0] * base[0][0]) << '\n';
}
int main(void) {
ios_base::sync_with_stdio(false); cin.tie(nullptr); // cout.tie(nullptr);
file("startrek");
// int t; cin >> t; while (t--)
process();
// cerr << "Time elapsed: " << TIME << " s.\n";
return (0^0);
}
Compilation message
startrek.cpp: In function 'void process()':
startrek.cpp:281:39: warning: narrowing conversion of 'lst_lose.std::vector<int>::size()' from 'std::vector<int>::size_type' {aka 'long unsigned int'} to 'long long int' [-Wnarrowing]
281 | Matrix <Modular> base({{lst_lose.size(), 1LL * n * n}});
| ~~~~~~~~~~~~~^~
startrek.cpp: In function 'int main()':
startrek.cpp:30:61: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
30 | #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
startrek.cpp:292:2: note: in expansion of macro 'file'
292 | file("startrek");
| ^~~~
startrek.cpp:30:94: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
30 | #define file(name) if (fopen(name".inp", "r")) { freopen(name".inp", "r", stdin); freopen(name".out", "w", stdout); }
| ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
startrek.cpp:292:2: note: in expansion of macro 'file'
292 | file("startrek");
| ^~~~
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
344 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
344 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Incorrect |
1 ms |
348 KB |
Output isn't correct |
| 2 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
0 ms |
348 KB |
Output is correct |
| 4 |
Correct |
0 ms |
348 KB |
Output is correct |
| 5 |
Correct |
0 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
348 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
0 ms |
348 KB |
Output is correct |
| 4 |
Correct |
0 ms |
348 KB |
Output is correct |
| 5 |
Correct |
0 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
348 KB |
Output is correct |
| 7 |
Correct |
1 ms |
344 KB |
Output is correct |
| 8 |
Correct |
1 ms |
604 KB |
Output is correct |
| 9 |
Correct |
1 ms |
348 KB |
Output is correct |
| 10 |
Correct |
1 ms |
348 KB |
Output is correct |
| 11 |
Correct |
1 ms |
348 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
0 ms |
348 KB |
Output is correct |
| 4 |
Correct |
0 ms |
348 KB |
Output is correct |
| 5 |
Correct |
0 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
348 KB |
Output is correct |
| 7 |
Correct |
1 ms |
344 KB |
Output is correct |
| 8 |
Correct |
1 ms |
604 KB |
Output is correct |
| 9 |
Correct |
1 ms |
348 KB |
Output is correct |
| 10 |
Correct |
1 ms |
348 KB |
Output is correct |
| 11 |
Correct |
1 ms |
348 KB |
Output is correct |
| 12 |
Correct |
39 ms |
11728 KB |
Output is correct |
| 13 |
Correct |
57 ms |
16072 KB |
Output is correct |
| 14 |
Correct |
31 ms |
8664 KB |
Output is correct |
| 15 |
Correct |
35 ms |
8608 KB |
Output is correct |
| 16 |
Correct |
36 ms |
8396 KB |
Output is correct |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
0 ms |
348 KB |
Output is correct |
| 4 |
Correct |
0 ms |
348 KB |
Output is correct |
| 5 |
Correct |
0 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
348 KB |
Output is correct |
| 7 |
Correct |
1 ms |
344 KB |
Output is correct |
| 8 |
Correct |
1 ms |
604 KB |
Output is correct |
| 9 |
Correct |
1 ms |
348 KB |
Output is correct |
| 10 |
Correct |
1 ms |
348 KB |
Output is correct |
| 11 |
Correct |
1 ms |
348 KB |
Output is correct |
| 12 |
Correct |
0 ms |
348 KB |
Output is correct |
| 13 |
Incorrect |
1 ms |
348 KB |
Output isn't correct |
| 14 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
348 KB |
Output is correct |
| 2 |
Correct |
0 ms |
348 KB |
Output is correct |
| 3 |
Correct |
0 ms |
348 KB |
Output is correct |
| 4 |
Correct |
0 ms |
348 KB |
Output is correct |
| 5 |
Correct |
0 ms |
348 KB |
Output is correct |
| 6 |
Correct |
0 ms |
348 KB |
Output is correct |
| 7 |
Correct |
1 ms |
344 KB |
Output is correct |
| 8 |
Correct |
1 ms |
604 KB |
Output is correct |
| 9 |
Correct |
1 ms |
348 KB |
Output is correct |
| 10 |
Correct |
1 ms |
348 KB |
Output is correct |
| 11 |
Correct |
1 ms |
348 KB |
Output is correct |
| 12 |
Correct |
39 ms |
11728 KB |
Output is correct |
| 13 |
Correct |
57 ms |
16072 KB |
Output is correct |
| 14 |
Correct |
31 ms |
8664 KB |
Output is correct |
| 15 |
Correct |
35 ms |
8608 KB |
Output is correct |
| 16 |
Correct |
36 ms |
8396 KB |
Output is correct |
| 17 |
Correct |
0 ms |
348 KB |
Output is correct |
| 18 |
Incorrect |
1 ms |
348 KB |
Output isn't correct |
| 19 |
Halted |
0 ms |
0 KB |
- |
| # |
Verdict |
Execution time |
Memory |
Grader output |
| 1 |
Correct |
0 ms |
344 KB |
Output is correct |
| 2 |
Incorrect |
1 ms |
344 KB |
Output isn't correct |
| 3 |
Halted |
0 ms |
0 KB |
- |
