Problem p03175 (C++)

Buggy submission (status: Time Limit Exceeded):
#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define mk make_pair
#define fi first
#define se second
#define vll vector<ll>
#define pii pair<ll, ll>
#define vvll vector<vector<ll>>
#define pb push_back
#define sz(v) (v).size()
#define inf 1e18
#define md 1000000007
#define all(v) (v).begin(), (v).end()
#define rep(i, a, b) for (ll i = a; i < b; ++i)
#define tel(a)                                                                 \
  { cout << a << "\n"; }
#define tell(a, b)                                                             \
  { cout << a << " | " << b << "\n"; }
#define telll(a, b, c)                                                         \
  { cout << a << " | " << b << " | " << c << "\n"; }
#define teln(v, n)                                                             \
  {                                                                            \
    cout << "v- ";                                                             \
    rep(i, 0, n) cout << v[i] << " ";                                          \
    cout << "\n";                                                              \
  }
#define IOS                                                                    \
  ios_base::sync_with_stdio(false);                                            \
  cin.tie(0);                                                                  \
  cout.tie(0);
#define tihs                                                                   \
  if (fopen("inp.txt", "r"))                                                   \
    freopen("inp.txt", "r", stdin), freopen("out.txt", "w", stdout);
using namespace std;
#define TRACE

#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1> void __f(const char *name, Arg1 &&arg1) {
  cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char *names, Arg1 &&arg1, Args &&...args) {
  const char *comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
#else
#define trace(...)
#endif

#define M 100010

ll dp[M][2];
ll n;
vll g[M];
ll dfs(ll u, ll par, ll col) {
  ll ans = 1;
  for (auto v : g[u]) {
    if (v == par)
      continue;
    if (col)
      ans = (ans * (dfs(v, u, 0) + dfs(v, u, 1))) % md;
    else
      ans = (ans * dfs(v, u, 1)) % md;
  }
  return dp[u][col] = ans;
}
int main() {
  IOS;
  tihs;
  memset(dp, -1, sizeof(dp));
  cin >> n;
  rep(i, 0, n - 1) {
    ll u, v;
    cin >> u >> v;
    u--, v--;
    g[u].pb(v);
    g[v].pb(u);
  }
  ll ans = dfs(0, -1, 0) + dfs(0, -1, 1);
  ans %= md;
  cout << ans;

  return 0;
}

Fixed submission:
#include <bits/stdc++.h>
// #include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define mk make_pair
#define fi first
#define se second
#define vll vector<ll>
#define pii pair<ll, ll>
#define vvll vector<vector<ll>>
#define pb push_back
#define sz(v) (v).size()
#define inf 1e18
#define md 1000000007
#define all(v) (v).begin(), (v).end()
#define rep(i, a, b) for (ll i = a; i < b; ++i)
#define tel(a)                                                                 \
  { cout << a << "\n"; }
#define tell(a, b)                                                             \
  { cout << a << " | " << b << "\n"; }
#define telll(a, b, c)                                                         \
  { cout << a << " | " << b << " | " << c << "\n"; }
#define teln(v, n)                                                             \
  {                                                                            \
    cout << "v- ";                                                             \
    rep(i, 0, n) cout << v[i] << " ";                                          \
    cout << "\n";                                                              \
  }
#define IOS                                                                    \
  ios_base::sync_with_stdio(false);                                            \
  cin.tie(0);                                                                  \
  cout.tie(0);
#define tihs                                                                   \
  if (fopen("inp.txt", "r"))                                                   \
    freopen("inp.txt", "r", stdin), freopen("out.txt", "w", stdout);
using namespace std;
#define TRACE

#ifdef TRACE
#define trace(...) __f(#__VA_ARGS__, __VA_ARGS__)
template <typename Arg1> void __f(const char *name, Arg1 &&arg1) {
  cerr << name << " : " << arg1 << std::endl;
}
template <typename Arg1, typename... Args>
void __f(const char *names, Arg1 &&arg1, Args &&...args) {
  const char *comma = strchr(names + 1, ',');
  cerr.write(names, comma - names) << " : " << arg1 << " | ";
  __f(comma + 1, args...);
}
#else
#define trace(...)
#endif

#define M 100010

ll dp[M][2];
ll n;
vll g[M];
ll dfs(ll u, ll par, ll col) {
  if (dp[u][col] != -1)
    return dp[u][col];
  ll ans = 1;
  for (auto v : g[u]) {
    if (v == par)
      continue;
    if (col)
      ans = (ans * (dfs(v, u, 0) + dfs(v, u, 1))) % md;
    else
      ans = (ans * dfs(v, u, 1)) % md;
  }
  return dp[u][col] = ans;
}
int main() {
  IOS;
  tihs;
  memset(dp, -1, sizeof(dp));
  cin >> n;
  rep(i, 0, n - 1) {
    ll u, v;
    cin >> u >> v;
    u--, v--;
    g[u].pb(v);
    g[v].pb(u);
  }
  ll ans = dfs(0, -1, 0) + dfs(0, -1, 1);
  ans %= md;
  cout << ans;

  return 0;
}