Problem p02822 (C++)

Buggy submission (status: Runtime Error):
#include "bits/stdc++.h"
#define rep(i, n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 1000000007;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619

vector<int> to[100005];
mint ans;
int N;
int dfs(int v, int p = -1) {
  int res = 1;
  vector<int> ts;
  for (int e : to[v]) {
    if (p == e) {
      continue;
    }
    int t = dfs(e, v);
    res += t;
    ts.push_back(t);
  }
  if (-1 != p) {
    ts.push_back(N - res);
  }
  mint now = mint(2).pow(N - 1) - 1;
  for (int t : ts) {
    now -= mint(2).pow(t) - 1;
  }
  ans += now;
  return res;
}

int main() {
  cin >> N;
  for (int n = 0; n < N - 1; ++n) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    to[a].push_back(b);
    to[b].push_back(a);
  }
  dfs(0);
  ans /= mint(2).pow(N);
  cout << ans.x << endl;
  return 0;
}

Fixed submission:
#include "bits/stdc++.h"
#define rep(i, n) for (int i = 0; i < (n); ++i)
using namespace std;
using ll = long long;
using P = pair<int, int>;

// auto mod int
// https://youtu.be/L8grWxBlIZ4?t=9858
// https://youtu.be/ERZuLAxZffQ?t=4807 : optimize
// https://youtu.be/8uowVvQ_-Mo?t=1329 : division
const int mod = 1000000007;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x = 0) : x((x % mod + mod) % mod) {}
  mint operator-() const { return mint(-x); }
  mint &operator+=(const mint a) {
    if ((x += a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator-=(const mint a) {
    if ((x += mod - a.x) >= mod)
      x -= mod;
    return *this;
  }
  mint &operator*=(const mint a) {
    (x *= a.x) %= mod;
    return *this;
  }
  mint operator+(const mint a) const { return mint(*this) += a; }
  mint operator-(const mint a) const { return mint(*this) -= a; }
  mint operator*(const mint a) const { return mint(*this) *= a; }
  mint pow(ll t) const {
    if (!t)
      return 1;
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1)
      a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const { return pow(mod - 2); }
  mint &operator/=(const mint a) { return *this *= a.inv(); }
  mint operator/(const mint a) const { return mint(*this) /= a; }
};
istream &operator>>(istream &is, const mint &a) { return is >> a.x; }
ostream &operator<<(ostream &os, const mint &a) { return os << a.x; }
// combination mod prime
// https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619

vector<int> to[200005];
mint ans;
int N;
int dfs(int v, int p = -1) {
  int res = 1;
  vector<int> ts;
  for (int e : to[v]) {
    if (p == e) {
      continue;
    }
    int t = dfs(e, v);
    res += t;
    ts.push_back(t);
  }
  if (-1 != p) {
    ts.push_back(N - res);
  }
  mint now = mint(2).pow(N - 1) - 1;
  for (int t : ts) {
    now -= mint(2).pow(t) - 1;
  }
  ans += now;
  return res;
}

int main() {
  cin >> N;
  for (int n = 0; n < N - 1; ++n) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    to[a].push_back(b);
    to[b].push_back(a);
  }
  dfs(0);
  ans /= mint(2).pow(N);
  cout << ans.x << endl;
  return 0;
}