Problem p02822 (C++)

Buggy submission (status: Runtime Error):
#define _USE_MATH_DEFINES
#include <algorithm>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>
using namespace std;
#define MOD 1000000007
#define rep(i, m, n) for (int(i) = (int)(m); i < (int)(n); i++)
#define REP(i, n) rep(i, 0, n)
#define FOR(i, c)                                                              \
  for (decltype((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define ll long long
#define ull unsigned long long
#define all(hoge) (hoge).begin(), (hoge).end()
typedef pair<ll, ll> P;
const long long INF = 1LL << 60;
typedef vector<ll> Array;
typedef vector<Array> Matrix;
string operator*(const string &s, int k) {
  if (k == 0)
    return "";
  string p = (s + s) * (k / 2);
  if (k % 2 == 1)
    p += s;
  return p;
}

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

struct Edge { // グラフ
  ll to, cap, rev;
  Edge(ll _to, ll _cap, ll _rev) {
    to = _to;
    cap = _cap;
    rev = _rev;
  }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph &G, ll from, ll to, ll cap, bool revFlag,
              ll revCap) { // 最大フロー求める Ford-fulkerson
  G[from].push_back(Edge(to, cap, (ll)G[to].size()));
  if (revFlag)
    G[to].push_back(Edge(
        from, revCap, (ll)G[from].size() - 1)); // 最小カットの場合逆辺は0にする
}
ll max_flow_dfs(Graph &G, ll v, ll t, ll f, vector<bool> &used) {
  if (v == t)
    return f;
  used[v] = true;
  for (int i = 0; i < G[v].size(); ++i) {
    Edge &e = G[v][i];
    if (!used[e.to] && e.cap > 0) {
      ll d = max_flow_dfs(G, e.to, t, min(f, e.cap), used);
      if (d > 0) {
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}
// 二分グラフの最大マッチングを求めたりも出来る　また二部グラフの最大独立集合は頂点数-最大マッチングのサイズ
ll max_flow(Graph &G, ll s, ll t) // O(V(V+E))
{
  ll flow = 0;
  for (;;) {
    vector<bool> used(G.size());
    REP(i, used.size()) used[i] = false;
    ll f = max_flow_dfs(G, s, t, INF, used);
    if (f == 0) {
      return flow;
    }
    flow += f;
  }
}
void BellmanFord(Graph &G, ll s, Array &d, Array &negative) { // O(|E||V|)
  d.resize(G.size());
  negative.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  REP(i, d.size()) negative[i] = false;
  d[s] = 0;
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
        }
      }
    }
  }
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
          negative[G[i][j].to] = true;
        }
        if (negative[i] == true)
          negative[G[i][j].to] = true;
      }
    }
  }
}
void Dijkstra(Graph &G, ll s, Array &d) { // O(|E|log|V|)
  d.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  d[s] = 0;
  priority_queue<P, vector<P>, greater<P>> q;
  q.push(make_pair(0, s));
  while (!q.empty()) {
    P a = q.top();
    q.pop();
    if (d[a.second] < a.first)
      continue;
    REP(i, G[a.second].size()) {
      Edge e = G[a.second][i];
      if (d[e.to] > d[a.second] + e.cap) {
        d[e.to] = d[a.second] + e.cap;
        q.push(make_pair(d[e.to], e.to));
      }
    }
  }
}
void WarshallFloyd(Graph &G, Matrix &d) { // O(V^3)
  d.resize(G.size());
  REP(i, d.size()) d[i].resize(G.size());
  REP(i, d.size()) {
    REP(j, d[i].size()) { d[i][j] = INF; }
  }
  REP(i, G.size()) {
    REP(j, G[i].size()) { d[i][G[i][j].to] = G[i][j].cap; }
  }
  REP(i, G.size()) {
    REP(j, G.size()) {
      REP(k, G.size()) { chmin(d[j][k], d[j][i] + d[i][k]); }
    }
  }
}
bool tsort(Graph &graph, vector<int> &order) { // トポロジカルソートO(E+V)
  int n = graph.size(), k = 0;
  Array in(n);
  for (auto &es : graph)
    for (auto &e : es)
      in[e.to]++;
  priority_queue<ll, Array, greater<ll>> que;
  REP(i, n)
  if (in[i] == 0)
    que.push(i);
  while (que.size()) {
    int v = que.top();
    que.pop();
    order.push_back(v);
    for (auto &e : graph[v])
      if (--in[e.to] == 0)
        que.push(e.to);
  }
  if (order.size() != n)
    return false;
  else
    return true;
}
class lca {
public:
  const int n = 0;
  const int log2_n = 0;
  std::vector<std::vector<int>> parent;
  std::vector<int> depth;

  lca() {}

  lca(const Graph &g, int root)
      : n(g.size()), log2_n(log2(n) + 1), parent(log2_n, std::vector<int>(n)),
        depth(n) {
    dfs(g, root, -1, 0);
    for (int k = 0; k + 1 < log2_n; k++) {
      for (int v = 0; v < (int)g.size(); v++) {
        if (parent[k][v] < 0)
          parent[k + 1][v] = -1;
        else
          parent[k + 1][v] = parent[k][parent[k][v]];
      }
    }
  }

  void dfs(const Graph &g, int v, int p, int d) {
    parent[0][v] = p;
    depth[v] = d;
    for (auto &e : g[v]) {
      if (e.to != p)
        dfs(g, e.to, v, d + 1);
    }
  }

  int get(int u, int v) {
    if (depth[u] > depth[v])
      std::swap(u, v);
    for (int k = 0; k < log2_n; k++) {
      if ((depth[v] - depth[u]) >> k & 1) {
        v = parent[k][v];
      }
    }
    if (u == v)
      return u;
    for (int k = log2_n - 1; k >= 0; k--) {
      if (parent[k][u] != parent[k][v]) {
        u = parent[k][u];
        v = parent[k][v];
      }
    }
    return parent[0][u];
  }
};
void visit(const Graph &g, int v, Matrix &scc, stack<ll> &S, Array &inS,
           Array &low, Array &num, int &time) {
  low[v] = num[v] = ++time;
  S.push(v);
  inS[v] = true;
  FOR(e, g[v]) {
    int w = e->to;
    if (num[w] == 0) {
      visit(g, w, scc, S, inS, low, num, time);
      low[v] = min(low[v], low[w]);
    } else if (inS[w])
      low[v] = min(low[v], num[w]);
  }
  if (low[v] == num[v]) {
    scc.push_back(Array());
    while (1) {
      int w = S.top();
      S.pop();
      inS[w] = false;
      scc.back().push_back(w);
      if (v == w)
        break;
    }
  }
}
void stronglyConnectedComponents(const Graph &g,
                                 Matrix &scc) { // 強連結成分分解 O(E+V)
  const int n = g.size();
  Array num(n), low(n);
  stack<ll> S;
  Array inS(n);
  int time = 0;
  REP(u, n) if (num[u] == 0) visit(g, u, scc, S, inS, low, num, time);
}

class UnionFind {
  vector<int> data;
  ll num;

public:
  UnionFind(int size) : data(size, -1), num(size) {}
  bool unite(int x, int y) { // xとyの集合を統合する
    x = root(x);
    y = root(y);
    if (x != y) {
      if (data[y] < data[x])
        swap(x, y);
      data[x] += data[y];
      data[y] = x;
    }
    num -= (x != y);
    return x != y;
  }
  bool findSet(int x, int y) { // xとyが同じ集合か返す
    return root(x) == root(y);
  }
  int root(int x) { // xのルートを返す
    return data[x] < 0 ? x : data[x] = root(data[x]);
  }
  int size(int x) { // xの集合のサイズを返す
    return -data[root(x)];
  }
  int numSet() { // 集合の数を返す
    return num;
  }
};
class SumSegTree {
private:
  ll _sum(ll a, ll b, ll k, ll l, ll r) {
    if (r <= a || b <= l)
      return 0; // 交差しない
    if (a <= l && r <= b)
      return dat[k]; // a,l,r,bの順で完全に含まれる
    else {
      ll s1 = _sum(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
      ll s2 = _sum(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
      return s1 + s2;
    }
  }

public:
  ll n, height;
  vector<ll> dat;

  // 初期化（_nは最大要素数）
  SumSegTree(ll _n) {
    n = 1;
    height = 1;
    while (n < _n) {
      n *= 2;
      height++;
    }
    dat = vector<ll>(2 * n - 1, 0);
  }

  // 場所i(0-indexed)にxを足す
  void add(ll i, ll x) {
    i += n - 1; // i番目の葉ノードへ
    dat[i] += x;
    while (i > 0) { // 下から上がっていく
      i = (i - 1) / 2;
      dat[i] += x;
    }
  }

  // 区間[a,b)の総和。ノードk=[l,r)に着目している。
  ll sum(ll a, ll b) { return _sum(a, b, 0, 0, n); }
};
class RmqTree {
private:
  ll _find(ll a, ll b, ll k, ll l, ll r) {
    if (r <= a || b <= l)
      return INF; // 交差しない
    if (a <= l && r <= b)
      return dat[k]; // a,l,r,bの順で完全に含まれる
    else {
      ll s1 = _find(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
      ll s2 = _find(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
      return min(s1, s2);
    }
  }

public:
  ll n, height;
  vector<ll> dat;

  // 初期化（_nは最大要素数）
  RmqTree(ll _n) {
    n = 1;
    height = 1;
    while (n < _n) {
      n *= 2;
      height++;
    }
    dat = vector<ll>(2 * n - 1, INF);
  }

  // 場所i(0-indexed)をxにする
  void update(ll i, ll x) {
    i += n - 1; // i番目の葉ノードへ
    dat[i] = x;
    while (i > 0) { // 下から上がっていく
      i = (i - 1) / 2;
      dat[i] = min(dat[i * 2 + 1], dat[i * 2 + 2]);
    }
  }

  // 区間[a,b)の最小値。ノードk=[l,r)に着目している。
  ll find(ll a, ll b) { return _find(a, b, 0, 0, n); }
};

// 約数求める //約数
void divisor(ll n, vector<ll> &ret) {
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i * i != n)
        ret.push_back(n / i);
    }
  }
  sort(ret.begin(), ret.end());
}

void divisor_prime(ll n, vector<P> &ret) {
  for (ll i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back({i, 0});
      while (n % i == 0) {
        n /= i;
        ret[ret.size() - 1].second++;
      }
    }
  }
  if (n != 1)
    ret.push_back({n, 1});
}

vector<ll> lis_fast(const vector<ll> &a) { // 最長部分増加列
  const ll n = a.size();
  vector<ll> A(n, INT_MAX);
  vector<ll> id(n);
  for (int i = 0; i < n; ++i) {
    id[i] = distance(A.begin(), lower_bound(A.begin(), A.end(), a[i]));
    A[id[i]] = a[i];
  }
  ll m = *max_element(id.begin(), id.end());
  vector<ll> b(m + 1);
  for (int i = n - 1; i >= 0; --i)
    if (id[i] == m)
      b[m--] = a[i];
  return b;
}

bool z_algorithm(string &str, vector<int> &z,
                 ll s) { // s&tを渡してtにsが含まれるかを返す
  const int L = str.size();
  z.resize(str.size());
  for (int i = 1, left = 0, right = 0; i < L; i++) {
    if (i > right) {
      left = right = i;
      for (; right < L && str[right - left] == str[right]; right++)
        ;
      z[i] = right - left;
      right--;
    } else {
      int k = i - left;
      if (z[k] < right - i + 1) {
        z[i] = z[k];
      } else {
        left = i;
        for (; right < L && str[right - left] == str[right]; right++)
          ;
        z[i] = right - left;
        right--;
      }
    }
    if (z[i] == s)
      return true;
  }
  return false;
}
bool z_algorithm(string &str,
                 vector<int> &z) { // z[i]==|s|のときstr[i]からsが含まれる
  const int L = str.size();
  z.resize(str.size());
  for (int i = 1, left = 0, right = 0; i < L; i++) {
    if (i > right) {
      left = right = i;
      for (; right < L && str[right - left] == str[right]; right++)
        ;
      z[i] = right - left;
      right--;
    } else {
      int k = i - left;
      if (z[k] < right - i + 1) {
        z[i] = z[k];
      } else {
        left = i;
        for (; right < L && str[right - left] == str[right]; right++)
          ;
        z[i] = right - left;
        right--;
      }
    }
  }
  return true;
}
// ローリングハッシュ
// 二分探索で LCP を求める機能つき
struct RollingHash {
  static const int base1 = 1007, base2 = 2009;
  static const int mod1 = 1000000007, mod2 = 1000000009;
  vector<long long> hash1, hash2, power1, power2;

  // construct
  RollingHash(const string &S) {
    int n = (int)S.size();
    hash1.assign(n + 1, 0);
    hash2.assign(n + 1, 0);
    power1.assign(n + 1, 1);
    power2.assign(n + 1, 1);
    for (int i = 0; i < n; ++i) {
      hash1[i + 1] = (hash1[i] * base1 + S[i]) % mod1;
      hash2[i + 1] = (hash2[i] * base2 + S[i]) % mod2;
      power1[i + 1] = (power1[i] * base1) % mod1;
      power2[i + 1] = (power2[i] * base2) % mod2;
    }
  }

  // get hash of S[left:right]
  inline pair<long long, long long> get(int l, int r) const {
    long long res1 = hash1[r] - hash1[l] * power1[r - l] % mod1;
    if (res1 < 0)
      res1 += mod1;
    long long res2 = hash2[r] - hash2[l] * power2[r - l] % mod2;
    if (res2 < 0)
      res2 += mod2;
    return {res1, res2};
  }

  // get lcp of S[a:] and T[b:]
  inline int getLCP(int a, int b) const {
    int len = min((int)hash1.size() - a, (int)hash1.size() - b);
    int low = 0, high = len;
    while (high - low > 1) {
      int mid = (low + high) >> 1;
      if (get(a, a + mid) != get(b, b + mid))
        high = mid;
      else
        low = mid;
    }
    return low;
  }
};

ll mod_pow(ll x, ll n, ll mod) {
  ll res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return res;
}

ll mod_inv(ll x, ll mod) { return mod_pow(x, mod - 2, mod); }
// nCrとか
class Combination {
public:
  Array fact;
  Array inv;
  ll mod;
  ll mod_inv(ll x) {
    ll n = mod - 2LL;
    ll res = 1LL;
    while (n > 0) {
      if (n & 1)
        res = res * x % mod;
      x = x * x % mod;
      n >>= 1;
    }
    return res;
  }
  ll nCr(ll n, ll r) { return ((fact[n] * inv[r] % mod) * inv[n - r]) % mod; }
  ll nPr(ll n, ll r) { return (fact[n] * inv[n - r]) % mod; }
  ll nHr(ll n, ll r) { return nCr(r + n - 1, r); }
  Combination(ll n, ll _mod) {
    mod = _mod;
    fact.resize(n + 1);
    fact[0] = 1;
    REP(i, n) { fact[i + 1] = (fact[i] * (i + 1LL)) % mod; }
    inv.resize(n + 1);
    inv[n] = mod_inv(fact[n]);
    for (int i = n; i > 0; i--) {
      inv[i - 1] = inv[i] * i % mod;
    }
  }
};

ll gcd(ll m, ll n) {
  if (n == 0)
    return m;
  return gcd(n, m % n);
} // gcd

ll lcm(ll m, ll n) { return m / gcd(m, n) * n; }

Matrix mIdentity(ll n) {
  Matrix A(n, Array(n));
  for (int i = 0; i < n; ++i)
    A[i][i] = 1;
  return A;
}

Matrix mMul(const Matrix &A, const Matrix &B) {
  Matrix C(A.size(), Array(B[0].size()));
  for (int i = 0; i < C.size(); ++i)
    for (int j = 0; j < C[i].size(); ++j)
      for (int k = 0; k < A[i].size(); ++k)
        (C[i][j] += (A[i][k] % MOD) * (B[k][j] % MOD)) %= MOD;
  return C;
}
// O( n^3 log e )
Matrix mPow(const Matrix &A, ll e) {
  return e == 0       ? mIdentity(A.size())
         : e % 2 == 0 ? mPow(mMul(A, A), e / 2)
                      : mMul(A, mPow(A, e - 1));
}

template <class T> class RectangleSum {
public:
  vector<vector<T>> sum;
  T GetSum(int left, int right, int top,
           int bottom) { //[left, right], [top, bottom]
    T res = sum[bottom][right];
    if (left > 0)
      res -= sum[bottom][left - 1];
    if (top > 0)
      res -= sum[top - 1][right];
    if (left > 0 && top > 0)
      res += sum[top - 1][left - 1];
    return res;
  }
  RectangleSum(const vector<vector<T>> &s, int h, int w) {
    sum.resize(h);
    for (int i = 0; i < h; i++)
      sum[i].resize(w, 0);
    for (int y = 0; y < h; y++) {
      for (int x = 0; x < w; x++) {
        sum[y][x] = s[y][x];
        if (y > 0)
          sum[y][x] += sum[y - 1][x];
        if (x > 0)
          sum[y][x] += sum[y][x - 1];
        if (y > 0 && x > 0)
          sum[y][x] -= sum[y - 1][x - 1];
      }
    }
  }
};

// NTT
ll _garner(Array &xs, Array &mods) {
  int M = xs.size();

  Array coeffs(M, 1), constants(M, 0);

  for (int i = 0; i < M - 1; ++i) {
    ll mod_i = mods[i];
    // coffs[i] * v + constants[i] == mr[i].val (mod mr[i].first) を解く
    ll v = (xs[i] - constants[i] + mod_i) % mod_i;
    v = (v * mod_pow(coeffs[i], mod_i - 2, mod_i)) % mod_i;

    for (int j = i + 1; j < M; j++) {
      ll mod_j = mods[j];
      constants[j] = (constants[j] + coeffs[j] * v) % mod_j;
      coeffs[j] = (coeffs[j] * mod_i) % mod_j;
    }
  }

  return constants.back();
}

template <typename T> inline void bit_reverse(vector<T> &a) {
  int n = a.size();
  int i = 0;
  for (int j = 1; j < n - 1; ++j) {
    for (int k = n >> 1; k > (i ^= k); k >>= 1)
      ;
    if (j < i)
      swap(a[i], a[j]);
  }
}

template <long long mod, long long primitive_root> class NTT {
public:
  long long get_mod() { return mod; }

  void _ntt(vector<long long> &a, int sign) {
    const int n = a.size();
    assert((n ^ (n & -n)) == 0); // n = 2^k

    const long long g = primitive_root; // g is primitive root of mod

    long long tmp = (mod - 1) * mod_pow((ll)n, mod - 2, mod) % mod; // -1/n
    long long h = mod_pow(g, tmp, mod);                             // ^n√g
    if (sign == -1)
      h = mod_pow(h, mod - 2, mod);

    bit_reverse(a);

    for (int m = 1; m < n; m <<= 1) {
      const int m2 = 2 * m;
      long long _base = mod_pow((ll)h, (ll)(n / m2), mod);
      long long _w = 1;
      for (int x = 0; x < m; ++x) {
        for (int s = x; s < n; s += m2) {
          long long u = a[s];
          long long d = (a[s + m] * _w) % mod;
          a[s] = (u + d) % mod;
          a[s + m] = (u - d + mod) % mod;
        }
        _w = (_w * _base) % mod;
      }
    }
  }
  void ntt(vector<long long> &input) { _ntt(input, 1); }
  void intt(vector<long long> &input) {
    _ntt(input, -1);

    const long long n_inv = mod_pow((ll)input.size(), mod - 2, mod);
    for (auto &x : input)
      x = (x * n_inv) % mod;
  }

  // 畳み込み演算を行う
  vector<long long> convolution(const vector<long long> &a,
                                const vector<long long> &b) {
    int result_size = a.size() + b.size() - 1;
    int n = 1;
    while (n < result_size)
      n <<= 1;

    vector<long long> _a = a, _b = b;
    _a.resize(n, 0);
    _b.resize(n, 0);

    ntt(_a);
    ntt(_b);
    for (int i = 0; i < n; ++i)
      _a[i] = (_a[i] * _b[i]) % mod;
    intt(_a);

    _a.resize(result_size);
    return _a;
  }
};

vector<long long> convolution_ntt(vector<long long> &a, vector<long long> &b,
                                  long long mod = 1224736769LL) {
  for (auto &x : a)
    x %= mod;
  for (auto &x : b)
    x %= mod;

  ll maxval = max(a.size(), b.size()) * *max_element(a.begin(), a.end()) *
              *max_element(b.begin(), b.end());
  if (maxval < 1224736769) {
    NTT<1224736769, 3> ntt3;
    return ntt3.convolution(a, b);
  }

  NTT<167772161, 3> ntt1;
  NTT<469762049, 3> ntt2;
  NTT<1224736769, 3> ntt3;

  vector<long long> x1 = ntt1.convolution(a, b);
  vector<long long> x2 = ntt2.convolution(a, b);
  vector<long long> x3 = ntt3.convolution(a, b);

  vector<long long> ret(x1.size());
  vector<long long> mods{167772161, 469762049, 1224736769, mod};
  for (int i = 0; i < x1.size(); ++i) {
    vector<long long> xs{x1[i], x2[i], x3[i], 0};
    ret[i] = _garner(xs, mods);
  }

  return ret;
}

int popcount3(int x) {
  x = (x & 0x55555555) + (x >> 1 & 0x55555555);
  x = (x & 0x33333333) + (x >> 2 & 0x33333333);
  x = (x & 0x0F0F0F0F) + (x >> 4 & 0x0F0F0F0F);
  x = (x & 0x00FF00FF) + (x >> 8 & 0x00FF00FF);
  x = (x & 0x0000FFFF) + (x >> 16 & 0x0000FFFF);

  return x;
}

template <typename T>
void rowReduction(vector<T> mat, vector<T> &basis) { // 掃き出し法
  for (auto e : mat) {
    for (auto b : basis)
      chmin(e, e ^ b);
    if (e)
      basis.push_back(e);
  }
  sort(all(basis), greater<T>());
}

/*
const ll mod = 998244353;
class SegmentTree {
private:
        int n;
        Array node[2];

public:
        SegmentTree(Array &v) {
                int sz = v.size();
                n = 1; while (n < sz)n *= 2;
                node[0].resize(2*n-1,1);
                node[1].resize(2*n-1,1);
                REP(i, sz) {
                        node[0][i + n - 1] = mod_inv(v[i],mod) * 100 % mod;
                        node[1][i + n - 1] = node[0][i + n - 1];
                }
                for (int i = n - 2; i >= 0; i--) {
                        node[0][i] = node[0][i * 2 + 1] * node[0][i * 2 + 2] %
mod; node[1][i] = (node[1][i * 2 + 1] * node[0][i * 2 + 2] + node[1][i * 2 + 2])
% mod;
                }
        }
        P getSum(int a, int b, int k = 0, int l = 0, int r = -1) {
                if (r < 0)r = n;
                if (r <= a || b <= l)return { 1,0 };
                if (a <= l && r <= b)return { node[0][k],node[1][k] };

                P vl = getSum(a, b, 2 * k + 1, l, (l + r) / 2);
                P vr = getSum(a, b, 2 * k + 2, (l + r) / 2, r);
                P ret = { vl.first * vr.first % mod ,(vl.second * vr.first +
vr.second) % mod }; return ret;
        }
};
*/

/*
string s, t;
        cin >> s >> t;
        REP(i, 210)REP(j, 210)REP(k, 210)dp[i][j][k] = INF;
        s.push_back('_'); t.push_back('_');
        dp[0][0][0] = 0;
        REP(i, s.size()+1) {
                REP(j, t.size() + 1) {
                        REP(k, 201) {
                                if (dp[i][j][k] == INF)continue;
                                ll nextS = i;
                                ll nextT = j;
                                if (s[i] == '(')nextS++;
                                if (t[j] == '(')nextT++;
                                chmin(dp[nextS][nextT][k + 1], dp[i][j][k] + 1);

                                if (k != 0) {

                                }
                        }
                }
        }


*/

ll two_inv[101010];

P dfs(Graph &graph, ll v, ll par) {
  P ret = {0, 1};

  Array kid;
  REP(i, graph[v].size()) {
    ll to = graph[v][i].to;
    if (to != par) {
      P temp = dfs(graph, to, v);
      ret.second += temp.second;
      (ret.first += temp.first) %= MOD;
      kid.push_back(temp.second);
    }
  }
  if (ret.second != graph.size())
    kid.push_back(graph.size() - ret.second);
  if (kid.size() < 2)
    return ret;
  ll temp = (1 + MOD - two_inv[graph.size() - 1]) % MOD;
  REP(i, kid.size()) {
    ll a = two_inv[graph.size() - 1];
    (a *= mod_inv(two_inv[kid[i]], MOD)) %= MOD;
    a *= (1 + MOD - two_inv[kid[i]]) % MOD;
    a %= MOD;
    (temp += MOD - a) %= MOD;
  }
  (temp *= mod_inv(2, MOD)) %= MOD;
  (ret.first += temp) %= MOD;
  return ret;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  ll n;
  cin >> n;
  Graph graph(n);
  REP(i, n - 1) {
    ll a, b;
    cin >> a >> b;
    a--;
    b--;
    add_edge(graph, a, b, 1, true, 1);
  }
  two_inv[0] = 1;
  REP(i, n + 1) { two_inv[i + 1] = two_inv[i] * mod_inv(2, MOD) % MOD; }

  REP(i, n) {
    if (graph[i].size() == 1) {
      cout << dfs(graph, i, -1).first << endl;
      return 0;
    }
  }

  return 0;
}

Fixed submission:
#define _USE_MATH_DEFINES
#include <algorithm>
#include <bitset>
#include <cassert>
#include <climits>
#include <cmath>
#include <cstring>
#include <iomanip>
#include <iostream>
#include <limits>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <unordered_map>
#include <vector>
using namespace std;
#define MOD 1000000007
#define rep(i, m, n) for (int(i) = (int)(m); i < (int)(n); i++)
#define REP(i, n) rep(i, 0, n)
#define FOR(i, c)                                                              \
  for (decltype((c).begin()) i = (c).begin(); i != (c).end(); ++i)
#define ll long long
#define ull unsigned long long
#define all(hoge) (hoge).begin(), (hoge).end()
typedef pair<ll, ll> P;
const long long INF = 1LL << 60;
typedef vector<ll> Array;
typedef vector<Array> Matrix;
string operator*(const string &s, int k) {
  if (k == 0)
    return "";
  string p = (s + s) * (k / 2);
  if (k % 2 == 1)
    p += s;
  return p;
}

template <class T> inline bool chmin(T &a, T b) {
  if (a > b) {
    a = b;
    return true;
  }
  return false;
}
template <class T> inline bool chmax(T &a, T b) {
  if (a < b) {
    a = b;
    return true;
  }
  return false;
}

struct Edge { // グラフ
  ll to, cap, rev;
  Edge(ll _to, ll _cap, ll _rev) {
    to = _to;
    cap = _cap;
    rev = _rev;
  }
};
typedef vector<Edge> Edges;
typedef vector<Edges> Graph;
void add_edge(Graph &G, ll from, ll to, ll cap, bool revFlag,
              ll revCap) { // 最大フロー求める Ford-fulkerson
  G[from].push_back(Edge(to, cap, (ll)G[to].size()));
  if (revFlag)
    G[to].push_back(Edge(
        from, revCap, (ll)G[from].size() - 1)); // 最小カットの場合逆辺は0にする
}
ll max_flow_dfs(Graph &G, ll v, ll t, ll f, vector<bool> &used) {
  if (v == t)
    return f;
  used[v] = true;
  for (int i = 0; i < G[v].size(); ++i) {
    Edge &e = G[v][i];
    if (!used[e.to] && e.cap > 0) {
      ll d = max_flow_dfs(G, e.to, t, min(f, e.cap), used);
      if (d > 0) {
        e.cap -= d;
        G[e.to][e.rev].cap += d;
        return d;
      }
    }
  }
  return 0;
}
// 二分グラフの最大マッチングを求めたりも出来る　また二部グラフの最大独立集合は頂点数-最大マッチングのサイズ
ll max_flow(Graph &G, ll s, ll t) // O(V(V+E))
{
  ll flow = 0;
  for (;;) {
    vector<bool> used(G.size());
    REP(i, used.size()) used[i] = false;
    ll f = max_flow_dfs(G, s, t, INF, used);
    if (f == 0) {
      return flow;
    }
    flow += f;
  }
}
void BellmanFord(Graph &G, ll s, Array &d, Array &negative) { // O(|E||V|)
  d.resize(G.size());
  negative.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  REP(i, d.size()) negative[i] = false;
  d[s] = 0;
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
        }
      }
    }
  }
  REP(k, G.size() - 1) {
    REP(i, G.size()) {
      REP(j, G[i].size()) {
        if (d[i] != INF && d[G[i][j].to] > d[i] + G[i][j].cap) {
          d[G[i][j].to] = d[i] + G[i][j].cap;
          negative[G[i][j].to] = true;
        }
        if (negative[i] == true)
          negative[G[i][j].to] = true;
      }
    }
  }
}
void Dijkstra(Graph &G, ll s, Array &d) { // O(|E|log|V|)
  d.resize(G.size());
  REP(i, d.size()) d[i] = INF;
  d[s] = 0;
  priority_queue<P, vector<P>, greater<P>> q;
  q.push(make_pair(0, s));
  while (!q.empty()) {
    P a = q.top();
    q.pop();
    if (d[a.second] < a.first)
      continue;
    REP(i, G[a.second].size()) {
      Edge e = G[a.second][i];
      if (d[e.to] > d[a.second] + e.cap) {
        d[e.to] = d[a.second] + e.cap;
        q.push(make_pair(d[e.to], e.to));
      }
    }
  }
}
void WarshallFloyd(Graph &G, Matrix &d) { // O(V^3)
  d.resize(G.size());
  REP(i, d.size()) d[i].resize(G.size());
  REP(i, d.size()) {
    REP(j, d[i].size()) { d[i][j] = INF; }
  }
  REP(i, G.size()) {
    REP(j, G[i].size()) { d[i][G[i][j].to] = G[i][j].cap; }
  }
  REP(i, G.size()) {
    REP(j, G.size()) {
      REP(k, G.size()) { chmin(d[j][k], d[j][i] + d[i][k]); }
    }
  }
}
bool tsort(Graph &graph, vector<int> &order) { // トポロジカルソートO(E+V)
  int n = graph.size(), k = 0;
  Array in(n);
  for (auto &es : graph)
    for (auto &e : es)
      in[e.to]++;
  priority_queue<ll, Array, greater<ll>> que;
  REP(i, n)
  if (in[i] == 0)
    que.push(i);
  while (que.size()) {
    int v = que.top();
    que.pop();
    order.push_back(v);
    for (auto &e : graph[v])
      if (--in[e.to] == 0)
        que.push(e.to);
  }
  if (order.size() != n)
    return false;
  else
    return true;
}
class lca {
public:
  const int n = 0;
  const int log2_n = 0;
  std::vector<std::vector<int>> parent;
  std::vector<int> depth;

  lca() {}

  lca(const Graph &g, int root)
      : n(g.size()), log2_n(log2(n) + 1), parent(log2_n, std::vector<int>(n)),
        depth(n) {
    dfs(g, root, -1, 0);
    for (int k = 0; k + 1 < log2_n; k++) {
      for (int v = 0; v < (int)g.size(); v++) {
        if (parent[k][v] < 0)
          parent[k + 1][v] = -1;
        else
          parent[k + 1][v] = parent[k][parent[k][v]];
      }
    }
  }

  void dfs(const Graph &g, int v, int p, int d) {
    parent[0][v] = p;
    depth[v] = d;
    for (auto &e : g[v]) {
      if (e.to != p)
        dfs(g, e.to, v, d + 1);
    }
  }

  int get(int u, int v) {
    if (depth[u] > depth[v])
      std::swap(u, v);
    for (int k = 0; k < log2_n; k++) {
      if ((depth[v] - depth[u]) >> k & 1) {
        v = parent[k][v];
      }
    }
    if (u == v)
      return u;
    for (int k = log2_n - 1; k >= 0; k--) {
      if (parent[k][u] != parent[k][v]) {
        u = parent[k][u];
        v = parent[k][v];
      }
    }
    return parent[0][u];
  }
};
void visit(const Graph &g, int v, Matrix &scc, stack<ll> &S, Array &inS,
           Array &low, Array &num, int &time) {
  low[v] = num[v] = ++time;
  S.push(v);
  inS[v] = true;
  FOR(e, g[v]) {
    int w = e->to;
    if (num[w] == 0) {
      visit(g, w, scc, S, inS, low, num, time);
      low[v] = min(low[v], low[w]);
    } else if (inS[w])
      low[v] = min(low[v], num[w]);
  }
  if (low[v] == num[v]) {
    scc.push_back(Array());
    while (1) {
      int w = S.top();
      S.pop();
      inS[w] = false;
      scc.back().push_back(w);
      if (v == w)
        break;
    }
  }
}
void stronglyConnectedComponents(const Graph &g,
                                 Matrix &scc) { // 強連結成分分解 O(E+V)
  const int n = g.size();
  Array num(n), low(n);
  stack<ll> S;
  Array inS(n);
  int time = 0;
  REP(u, n) if (num[u] == 0) visit(g, u, scc, S, inS, low, num, time);
}

class UnionFind {
  vector<int> data;
  ll num;

public:
  UnionFind(int size) : data(size, -1), num(size) {}
  bool unite(int x, int y) { // xとyの集合を統合する
    x = root(x);
    y = root(y);
    if (x != y) {
      if (data[y] < data[x])
        swap(x, y);
      data[x] += data[y];
      data[y] = x;
    }
    num -= (x != y);
    return x != y;
  }
  bool findSet(int x, int y) { // xとyが同じ集合か返す
    return root(x) == root(y);
  }
  int root(int x) { // xのルートを返す
    return data[x] < 0 ? x : data[x] = root(data[x]);
  }
  int size(int x) { // xの集合のサイズを返す
    return -data[root(x)];
  }
  int numSet() { // 集合の数を返す
    return num;
  }
};
class SumSegTree {
private:
  ll _sum(ll a, ll b, ll k, ll l, ll r) {
    if (r <= a || b <= l)
      return 0; // 交差しない
    if (a <= l && r <= b)
      return dat[k]; // a,l,r,bの順で完全に含まれる
    else {
      ll s1 = _sum(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
      ll s2 = _sum(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
      return s1 + s2;
    }
  }

public:
  ll n, height;
  vector<ll> dat;

  // 初期化（_nは最大要素数）
  SumSegTree(ll _n) {
    n = 1;
    height = 1;
    while (n < _n) {
      n *= 2;
      height++;
    }
    dat = vector<ll>(2 * n - 1, 0);
  }

  // 場所i(0-indexed)にxを足す
  void add(ll i, ll x) {
    i += n - 1; // i番目の葉ノードへ
    dat[i] += x;
    while (i > 0) { // 下から上がっていく
      i = (i - 1) / 2;
      dat[i] += x;
    }
  }

  // 区間[a,b)の総和。ノードk=[l,r)に着目している。
  ll sum(ll a, ll b) { return _sum(a, b, 0, 0, n); }
};
class RmqTree {
private:
  ll _find(ll a, ll b, ll k, ll l, ll r) {
    if (r <= a || b <= l)
      return INF; // 交差しない
    if (a <= l && r <= b)
      return dat[k]; // a,l,r,bの順で完全に含まれる
    else {
      ll s1 = _find(a, b, 2 * k + 1, l, (l + r) / 2); // 左の子
      ll s2 = _find(a, b, 2 * k + 2, (l + r) / 2, r); // 右の子
      return min(s1, s2);
    }
  }

public:
  ll n, height;
  vector<ll> dat;

  // 初期化（_nは最大要素数）
  RmqTree(ll _n) {
    n = 1;
    height = 1;
    while (n < _n) {
      n *= 2;
      height++;
    }
    dat = vector<ll>(2 * n - 1, INF);
  }

  // 場所i(0-indexed)をxにする
  void update(ll i, ll x) {
    i += n - 1; // i番目の葉ノードへ
    dat[i] = x;
    while (i > 0) { // 下から上がっていく
      i = (i - 1) / 2;
      dat[i] = min(dat[i * 2 + 1], dat[i * 2 + 2]);
    }
  }

  // 区間[a,b)の最小値。ノードk=[l,r)に着目している。
  ll find(ll a, ll b) { return _find(a, b, 0, 0, n); }
};

// 約数求める //約数
void divisor(ll n, vector<ll> &ret) {
  for (ll i = 1; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back(i);
      if (i * i != n)
        ret.push_back(n / i);
    }
  }
  sort(ret.begin(), ret.end());
}

void divisor_prime(ll n, vector<P> &ret) {
  for (ll i = 2; i * i <= n; i++) {
    if (n % i == 0) {
      ret.push_back({i, 0});
      while (n % i == 0) {
        n /= i;
        ret[ret.size() - 1].second++;
      }
    }
  }
  if (n != 1)
    ret.push_back({n, 1});
}

vector<ll> lis_fast(const vector<ll> &a) { // 最長部分増加列
  const ll n = a.size();
  vector<ll> A(n, INT_MAX);
  vector<ll> id(n);
  for (int i = 0; i < n; ++i) {
    id[i] = distance(A.begin(), lower_bound(A.begin(), A.end(), a[i]));
    A[id[i]] = a[i];
  }
  ll m = *max_element(id.begin(), id.end());
  vector<ll> b(m + 1);
  for (int i = n - 1; i >= 0; --i)
    if (id[i] == m)
      b[m--] = a[i];
  return b;
}

bool z_algorithm(string &str, vector<int> &z,
                 ll s) { // s&tを渡してtにsが含まれるかを返す
  const int L = str.size();
  z.resize(str.size());
  for (int i = 1, left = 0, right = 0; i < L; i++) {
    if (i > right) {
      left = right = i;
      for (; right < L && str[right - left] == str[right]; right++)
        ;
      z[i] = right - left;
      right--;
    } else {
      int k = i - left;
      if (z[k] < right - i + 1) {
        z[i] = z[k];
      } else {
        left = i;
        for (; right < L && str[right - left] == str[right]; right++)
          ;
        z[i] = right - left;
        right--;
      }
    }
    if (z[i] == s)
      return true;
  }
  return false;
}
bool z_algorithm(string &str,
                 vector<int> &z) { // z[i]==|s|のときstr[i]からsが含まれる
  const int L = str.size();
  z.resize(str.size());
  for (int i = 1, left = 0, right = 0; i < L; i++) {
    if (i > right) {
      left = right = i;
      for (; right < L && str[right - left] == str[right]; right++)
        ;
      z[i] = right - left;
      right--;
    } else {
      int k = i - left;
      if (z[k] < right - i + 1) {
        z[i] = z[k];
      } else {
        left = i;
        for (; right < L && str[right - left] == str[right]; right++)
          ;
        z[i] = right - left;
        right--;
      }
    }
  }
  return true;
}
// ローリングハッシュ
// 二分探索で LCP を求める機能つき
struct RollingHash {
  static const int base1 = 1007, base2 = 2009;
  static const int mod1 = 1000000007, mod2 = 1000000009;
  vector<long long> hash1, hash2, power1, power2;

  // construct
  RollingHash(const string &S) {
    int n = (int)S.size();
    hash1.assign(n + 1, 0);
    hash2.assign(n + 1, 0);
    power1.assign(n + 1, 1);
    power2.assign(n + 1, 1);
    for (int i = 0; i < n; ++i) {
      hash1[i + 1] = (hash1[i] * base1 + S[i]) % mod1;
      hash2[i + 1] = (hash2[i] * base2 + S[i]) % mod2;
      power1[i + 1] = (power1[i] * base1) % mod1;
      power2[i + 1] = (power2[i] * base2) % mod2;
    }
  }

  // get hash of S[left:right]
  inline pair<long long, long long> get(int l, int r) const {
    long long res1 = hash1[r] - hash1[l] * power1[r - l] % mod1;
    if (res1 < 0)
      res1 += mod1;
    long long res2 = hash2[r] - hash2[l] * power2[r - l] % mod2;
    if (res2 < 0)
      res2 += mod2;
    return {res1, res2};
  }

  // get lcp of S[a:] and T[b:]
  inline int getLCP(int a, int b) const {
    int len = min((int)hash1.size() - a, (int)hash1.size() - b);
    int low = 0, high = len;
    while (high - low > 1) {
      int mid = (low + high) >> 1;
      if (get(a, a + mid) != get(b, b + mid))
        high = mid;
      else
        low = mid;
    }
    return low;
  }
};

ll mod_pow(ll x, ll n, ll mod) {
  ll res = 1;
  while (n > 0) {
    if (n & 1)
      res = res * x % mod;
    x = x * x % mod;
    n >>= 1;
  }
  return res;
}

ll mod_inv(ll x, ll mod) { return mod_pow(x, mod - 2, mod); }
// nCrとか
class Combination {
public:
  Array fact;
  Array inv;
  ll mod;
  ll mod_inv(ll x) {
    ll n = mod - 2LL;
    ll res = 1LL;
    while (n > 0) {
      if (n & 1)
        res = res * x % mod;
      x = x * x % mod;
      n >>= 1;
    }
    return res;
  }
  ll nCr(ll n, ll r) { return ((fact[n] * inv[r] % mod) * inv[n - r]) % mod; }
  ll nPr(ll n, ll r) { return (fact[n] * inv[n - r]) % mod; }
  ll nHr(ll n, ll r) { return nCr(r + n - 1, r); }
  Combination(ll n, ll _mod) {
    mod = _mod;
    fact.resize(n + 1);
    fact[0] = 1;
    REP(i, n) { fact[i + 1] = (fact[i] * (i + 1LL)) % mod; }
    inv.resize(n + 1);
    inv[n] = mod_inv(fact[n]);
    for (int i = n; i > 0; i--) {
      inv[i - 1] = inv[i] * i % mod;
    }
  }
};

ll gcd(ll m, ll n) {
  if (n == 0)
    return m;
  return gcd(n, m % n);
} // gcd

ll lcm(ll m, ll n) { return m / gcd(m, n) * n; }

Matrix mIdentity(ll n) {
  Matrix A(n, Array(n));
  for (int i = 0; i < n; ++i)
    A[i][i] = 1;
  return A;
}

Matrix mMul(const Matrix &A, const Matrix &B) {
  Matrix C(A.size(), Array(B[0].size()));
  for (int i = 0; i < C.size(); ++i)
    for (int j = 0; j < C[i].size(); ++j)
      for (int k = 0; k < A[i].size(); ++k)
        (C[i][j] += (A[i][k] % MOD) * (B[k][j] % MOD)) %= MOD;
  return C;
}
// O( n^3 log e )
Matrix mPow(const Matrix &A, ll e) {
  return e == 0       ? mIdentity(A.size())
         : e % 2 == 0 ? mPow(mMul(A, A), e / 2)
                      : mMul(A, mPow(A, e - 1));
}

template <class T> class RectangleSum {
public:
  vector<vector<T>> sum;
  T GetSum(int left, int right, int top,
           int bottom) { //[left, right], [top, bottom]
    T res = sum[bottom][right];
    if (left > 0)
      res -= sum[bottom][left - 1];
    if (top > 0)
      res -= sum[top - 1][right];
    if (left > 0 && top > 0)
      res += sum[top - 1][left - 1];
    return res;
  }
  RectangleSum(const vector<vector<T>> &s, int h, int w) {
    sum.resize(h);
    for (int i = 0; i < h; i++)
      sum[i].resize(w, 0);
    for (int y = 0; y < h; y++) {
      for (int x = 0; x < w; x++) {
        sum[y][x] = s[y][x];
        if (y > 0)
          sum[y][x] += sum[y - 1][x];
        if (x > 0)
          sum[y][x] += sum[y][x - 1];
        if (y > 0 && x > 0)
          sum[y][x] -= sum[y - 1][x - 1];
      }
    }
  }
};

// NTT
ll _garner(Array &xs, Array &mods) {
  int M = xs.size();

  Array coeffs(M, 1), constants(M, 0);

  for (int i = 0; i < M - 1; ++i) {
    ll mod_i = mods[i];
    // coffs[i] * v + constants[i] == mr[i].val (mod mr[i].first) を解く
    ll v = (xs[i] - constants[i] + mod_i) % mod_i;
    v = (v * mod_pow(coeffs[i], mod_i - 2, mod_i)) % mod_i;

    for (int j = i + 1; j < M; j++) {
      ll mod_j = mods[j];
      constants[j] = (constants[j] + coeffs[j] * v) % mod_j;
      coeffs[j] = (coeffs[j] * mod_i) % mod_j;
    }
  }

  return constants.back();
}

template <typename T> inline void bit_reverse(vector<T> &a) {
  int n = a.size();
  int i = 0;
  for (int j = 1; j < n - 1; ++j) {
    for (int k = n >> 1; k > (i ^= k); k >>= 1)
      ;
    if (j < i)
      swap(a[i], a[j]);
  }
}

template <long long mod, long long primitive_root> class NTT {
public:
  long long get_mod() { return mod; }

  void _ntt(vector<long long> &a, int sign) {
    const int n = a.size();
    assert((n ^ (n & -n)) == 0); // n = 2^k

    const long long g = primitive_root; // g is primitive root of mod

    long long tmp = (mod - 1) * mod_pow((ll)n, mod - 2, mod) % mod; // -1/n
    long long h = mod_pow(g, tmp, mod);                             // ^n√g
    if (sign == -1)
      h = mod_pow(h, mod - 2, mod);

    bit_reverse(a);

    for (int m = 1; m < n; m <<= 1) {
      const int m2 = 2 * m;
      long long _base = mod_pow((ll)h, (ll)(n / m2), mod);
      long long _w = 1;
      for (int x = 0; x < m; ++x) {
        for (int s = x; s < n; s += m2) {
          long long u = a[s];
          long long d = (a[s + m] * _w) % mod;
          a[s] = (u + d) % mod;
          a[s + m] = (u - d + mod) % mod;
        }
        _w = (_w * _base) % mod;
      }
    }
  }
  void ntt(vector<long long> &input) { _ntt(input, 1); }
  void intt(vector<long long> &input) {
    _ntt(input, -1);

    const long long n_inv = mod_pow((ll)input.size(), mod - 2, mod);
    for (auto &x : input)
      x = (x * n_inv) % mod;
  }

  // 畳み込み演算を行う
  vector<long long> convolution(const vector<long long> &a,
                                const vector<long long> &b) {
    int result_size = a.size() + b.size() - 1;
    int n = 1;
    while (n < result_size)
      n <<= 1;

    vector<long long> _a = a, _b = b;
    _a.resize(n, 0);
    _b.resize(n, 0);

    ntt(_a);
    ntt(_b);
    for (int i = 0; i < n; ++i)
      _a[i] = (_a[i] * _b[i]) % mod;
    intt(_a);

    _a.resize(result_size);
    return _a;
  }
};

vector<long long> convolution_ntt(vector<long long> &a, vector<long long> &b,
                                  long long mod = 1224736769LL) {
  for (auto &x : a)
    x %= mod;
  for (auto &x : b)
    x %= mod;

  ll maxval = max(a.size(), b.size()) * *max_element(a.begin(), a.end()) *
              *max_element(b.begin(), b.end());
  if (maxval < 1224736769) {
    NTT<1224736769, 3> ntt3;
    return ntt3.convolution(a, b);
  }

  NTT<167772161, 3> ntt1;
  NTT<469762049, 3> ntt2;
  NTT<1224736769, 3> ntt3;

  vector<long long> x1 = ntt1.convolution(a, b);
  vector<long long> x2 = ntt2.convolution(a, b);
  vector<long long> x3 = ntt3.convolution(a, b);

  vector<long long> ret(x1.size());
  vector<long long> mods{167772161, 469762049, 1224736769, mod};
  for (int i = 0; i < x1.size(); ++i) {
    vector<long long> xs{x1[i], x2[i], x3[i], 0};
    ret[i] = _garner(xs, mods);
  }

  return ret;
}

int popcount3(int x) {
  x = (x & 0x55555555) + (x >> 1 & 0x55555555);
  x = (x & 0x33333333) + (x >> 2 & 0x33333333);
  x = (x & 0x0F0F0F0F) + (x >> 4 & 0x0F0F0F0F);
  x = (x & 0x00FF00FF) + (x >> 8 & 0x00FF00FF);
  x = (x & 0x0000FFFF) + (x >> 16 & 0x0000FFFF);

  return x;
}

template <typename T>
void rowReduction(vector<T> mat, vector<T> &basis) { // 掃き出し法
  for (auto e : mat) {
    for (auto b : basis)
      chmin(e, e ^ b);
    if (e)
      basis.push_back(e);
  }
  sort(all(basis), greater<T>());
}

/*
const ll mod = 998244353;
class SegmentTree {
private:
        int n;
        Array node[2];

public:
        SegmentTree(Array &v) {
                int sz = v.size();
                n = 1; while (n < sz)n *= 2;
                node[0].resize(2*n-1,1);
                node[1].resize(2*n-1,1);
                REP(i, sz) {
                        node[0][i + n - 1] = mod_inv(v[i],mod) * 100 % mod;
                        node[1][i + n - 1] = node[0][i + n - 1];
                }
                for (int i = n - 2; i >= 0; i--) {
                        node[0][i] = node[0][i * 2 + 1] * node[0][i * 2 + 2] %
mod; node[1][i] = (node[1][i * 2 + 1] * node[0][i * 2 + 2] + node[1][i * 2 + 2])
% mod;
                }
        }
        P getSum(int a, int b, int k = 0, int l = 0, int r = -1) {
                if (r < 0)r = n;
                if (r <= a || b <= l)return { 1,0 };
                if (a <= l && r <= b)return { node[0][k],node[1][k] };

                P vl = getSum(a, b, 2 * k + 1, l, (l + r) / 2);
                P vr = getSum(a, b, 2 * k + 2, (l + r) / 2, r);
                P ret = { vl.first * vr.first % mod ,(vl.second * vr.first +
vr.second) % mod }; return ret;
        }
};
*/

/*
string s, t;
        cin >> s >> t;
        REP(i, 210)REP(j, 210)REP(k, 210)dp[i][j][k] = INF;
        s.push_back('_'); t.push_back('_');
        dp[0][0][0] = 0;
        REP(i, s.size()+1) {
                REP(j, t.size() + 1) {
                        REP(k, 201) {
                                if (dp[i][j][k] == INF)continue;
                                ll nextS = i;
                                ll nextT = j;
                                if (s[i] == '(')nextS++;
                                if (t[j] == '(')nextT++;
                                chmin(dp[nextS][nextT][k + 1], dp[i][j][k] + 1);

                                if (k != 0) {

                                }
                        }
                }
        }


*/

ll two_inv[201010];

P dfs(Graph &graph, ll v, ll par) {
  P ret = {0, 1};

  Array kid;
  REP(i, graph[v].size()) {
    ll to = graph[v][i].to;
    if (to != par) {
      P temp = dfs(graph, to, v);
      ret.second += temp.second;
      (ret.first += temp.first) %= MOD;
      kid.push_back(temp.second);
    }
  }
  if (ret.second != graph.size())
    kid.push_back(graph.size() - ret.second);
  if (kid.size() < 2)
    return ret;
  ll temp = (1 + MOD - two_inv[graph.size() - 1]) % MOD;
  REP(i, kid.size()) {
    ll a = two_inv[graph.size() - 1];
    (a *= mod_inv(two_inv[kid[i]], MOD)) %= MOD;
    a *= (1 + MOD - two_inv[kid[i]]) % MOD;
    a %= MOD;
    (temp += MOD - a) %= MOD;
  }
  (temp *= mod_inv(2, MOD)) %= MOD;
  (ret.first += temp) %= MOD;
  return ret;
}

int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);

  ll n;
  cin >> n;
  Graph graph(n);
  REP(i, n - 1) {
    ll a, b;
    cin >> a >> b;
    a--;
    b--;
    add_edge(graph, a, b, 1, true, 1);
  }
  two_inv[0] = 1;
  REP(i, n + 1) { two_inv[i + 1] = two_inv[i] * mod_inv(2, MOD) % MOD; }

  REP(i, n) {
    if (graph[i].size() == 1) {
      cout << dfs(graph, i, -1).first << endl;
      return 0;
    }
  }

  return 0;
}