Problem:
Score : 600 points

Problem Statement

We have a tree with N vertices numbered 1 to N. The i-th edge in this tree connects Vertex a_i and b_i.
For each k=1, ..., N, solve the problem below:

Consider writing a number on each vertex in the tree in the following manner:

First, write 1 on Vertex k.

Then, for each of the numbers 2, ..., N in this order, write the number on the vertex chosen as follows:

Choose a vertex that still does not have a number written on it and is adjacent to a vertex with a number already written on it. If there are multiple such vertices, choose one of them at random.

Find the number of ways in which we can write the numbers on the vertices, modulo (10^9+7).

Constraints

2 \leq N \leq 2 \times 10^5

1 \leq a_i,b_i \leq N

The given graph is a tree.

Input

Input is given from Standard Input in the following format:

N
a_1 b_1
:
a_{N-1} b_{N-1}

Output

For each k=1, 2, ..., N in this order, print a line containing the answer to the problem.

Sample Input 1

3
1 2
1 3

Sample Output 1

2
1
1

The graph in this input is as follows:

For k=1, there are two ways in which we can write the numbers on the vertices, as follows:

Writing 1, 2, 3 on Vertex 1, 2, 3, respectively

Writing 1, 3, 2 on Vertex 1, 2, 3, respectively

Sample Input 2

2
1 2

Sample Output 2

1
1

The graph in this input is as follows:

Sample Input 3

5
1 2
2 3
3 4
3 5

Sample Output 3

2
8
12
3
3

The graph in this input is as follows:

Sample Input 4

8
1 2
2 3
3 4
3 5
3 6
6 7
6 8

Sample Output 4

40
280
840
120
120
504
72
72

The graph in this input is as follows:

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/**
 *    author:  zjsdut
 *    created: 2020/03/28 21:12:25
 **/
#include <bits/stdc++.h>

using namespace std;

struct fast_ios {
  fast_ios() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
  };
} fast_ios_;

template <typename A, typename B> bool chkmin(A &a, const B &b) {
  if (b < a) {
    a = b;
    return true;
  }
  return false;
}

template <typename A, typename B> bool chkmax(A &a, const B &b) {
  if (b > a) {
    a = b;
    return true;
  }
  return false;
}

template <typename T> istream &operator>>(istream &stream, vector<T> &vec) {
  for (auto &x : vec)
    stream >> x;
  return stream;
}

void scan() {}

template <class T, class... Args> void scan(T &a, Args &... rest) {
  cin >> a;
  scan(rest...);
}

using ll = long long;
using vl = vector<ll>;
using vb = vector<bool>;
using vi = vector<int>;
using pii = pair<int, int>;
template <typename T> using vv = vector<vector<T>>;
#define rng(i, a, b) for (int i = (int)(a); i < (int)(b); ++i)
#define up(i, a, b) for (int i = int(a); i <= int(b); ++i)
#define down(i, b, a) for (int i = int(b); i >= int(a); i--)
#define TOKENPASTE(x, y) x##y
#define TOKENPASTE2(x, y) TOKENPASTE(x, y)
#define rep(n)                                                                 \
  for (int TOKENPASTE2(_iter_, __LINE__) = 0,                                  \
                               TOKENPASTE2(_num_, __LINE__) = (int)(n);        \
       TOKENPASTE2(_iter_, __LINE__) < TOKENPASTE2(_num_, __LINE__);           \
       ++TOKENPASTE2(_iter_, __LINE__))
#define FOR(x, cont) for (const auto &x : cont)
#define For(x, cont) for (auto &x : cont)
#define all(x) begin(x), end(x)
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define ep emplace
#define SZ(x) (int)(x).size()
#define UNIQ(vec) (vec).erase(unique(all(vec)), end(vec))
#define LB(cont, x) int(lower_bound(all(cont), x) - begin(cont))
#define UB(cont, x) int(upper_bound(all(cont), x) - begin(cont))

template <typename T>
ostream &operator<<(ostream &stream, const vector<T> &vec) {
  if (!vec.empty()) {
    stream << vec[0];
    for (size_t i = 1; i != vec.size(); ++i)
      stream << ' ' << vec[i];
  }
  return stream;
}

template <typename T> void print(const vector<T> &t) { cout << t << '\n'; }

template <typename T> void print(const vector<vector<T>> &t) {
  for (const auto &row : t) {
    print(row);
  }
}

template <typename T> void print(const T &t) { cout << t << ' '; }

template <typename T, typename... Args>
void print(const T &t, const Args &... rest) {
  print(t);
  print(rest...);
}

template <typename T> void println(const T &t) { cout << t << '\n'; }

template <typename T, typename... Args>
void println(const T &t, const Args &... rest) {
  print(t);
  println(rest...);
}
// tourist's modular-arithmetic class
template <typename T> T inverse(T a, T m) {
  T u = 0, v = 1;
  while (a != 0) {
    T t = m / a;
    m -= t * a;
    swap(a, m);
    u -= t * v;
    swap(u, v);
  }
  assert(m == 1);
  return u;
}

template <typename T> class Modular {
public:
  using Type = typename decay<decltype(T::value)>::type;

  constexpr Modular() : value() {}

  template <typename U> Modular(const U &x) { value = normalize(x); }

  template <typename U> static Type normalize(const U &x) {
    Type v;
    if (-mod() <= x && x < mod())
      v = static_cast<Type>(x);
    else
      v = static_cast<Type>(x % mod());
    if (v < 0)
      v += mod();
    return v;
  }

  const Type &operator()() const { return value; }

  template <typename U> explicit operator U() const {
    return static_cast<U>(value);
  }

  constexpr static Type mod() { return T::value; }

  Modular &operator+=(const Modular &other) {
    if ((value += other.value) >= mod())
      value -= mod();
    return *this;
  }

  Modular &operator-=(const Modular &other) {
    if ((value -= other.value) < 0)
      value += mod();
    return *this;
  }

  template <typename U> Modular &operator+=(const U &other) {
    return *this += Modular(other);
  }

  template <typename U> Modular &operator-=(const U &other) {
    return *this -= Modular(other);
  }

  Modular &operator++() { return *this += 1; }

  Modular &operator--() { return *this -= 1; }

  Modular operator++(int) {
    Modular result(*this);
    *this += 1;
    return result;
  }

  Modular operator--(int) {
    Modular result(*this);
    *this -= 1;
    return result;
  }

  Modular operator-() const { return Modular(-value); }

  template <typename U = T>
  enable_if_t<is_same<typename Modular<U>::Type, int>::value, Modular> &
  operator*=(const Modular &rhs) {
#ifdef _WIN32
    uint64_t x = static_cast<int64_t>(value) * static_cast<int64_t>(rhs.value);
    uint32_t xh = static_cast<uint32_t>(x >> 32), xl = static_cast<uint32_t>(x),
             d, m;
    asm("divl %4; \n\t" : "=a"(d), "=d"(m) : "d"(xh), "a"(xl), "r"(mod()));
    value = m;
#else
    value = normalize(static_cast<int64_t>(value) *
                      static_cast<int64_t>(rhs.value));
#endif
    return *this;
  }

  template <typename U = T>
  enable_if_t<is_same<typename Modular<U>::Type, int64_t>::value, Modular> &
  operator*=(const Modular &rhs) {
    int64_t q = static_cast<int64_t>(static_cast<long double>(value) *
                                     rhs.value / mod());
    value = normalize(value * rhs.value - q * mod());
    return *this;
  }

  template <typename U = T>
  enable_if_t<!is_integral<typename Modular<U>::Type>::value, Modular> &
  operator*=(const Modular &rhs) {
    value = normalize(value * rhs.value);
    return *this;
  }

  Modular &operator/=(const Modular &other) {
    return *this *= Modular(inverse(other.value, mod()));
  }

  template <typename U> friend const Modular<U> &abs(const Modular<U> &v) {
    return v;
  }

  template <typename U>
  friend bool operator==(const Modular<U> &lhs, const Modular<U> &rhs);

  template <typename U>
  friend bool operator<(const Modular<U> &lhs, const Modular<U> &rhs);

  template <typename U>
  friend std::istream &operator>>(std::istream &stream, Modular<U> &number);

private:
  Type value;
};

template <typename T>
bool operator==(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value == rhs.value;
}

template <typename T, typename U>
bool operator==(const Modular<T> &lhs, U rhs) {
  return lhs == Modular<T>(rhs);
}

template <typename T, typename U>
bool operator==(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) == rhs;
}

template <typename T>
bool operator!=(const Modular<T> &lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}

template <typename T, typename U>
bool operator!=(const Modular<T> &lhs, U rhs) {
  return !(lhs == rhs);
}

template <typename T, typename U>
bool operator!=(U lhs, const Modular<T> &rhs) {
  return !(lhs == rhs);
}

template <typename T>
bool operator<(const Modular<T> &lhs, const Modular<T> &rhs) {
  return lhs.value < rhs.value;
}

template <typename T>
Modular<T> operator+(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}

template <typename T, typename U>
Modular<T> operator+(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) += rhs;
}

template <typename T, typename U>
Modular<T> operator+(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) += rhs;
}

template <typename T>
Modular<T> operator-(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}

template <typename T, typename U>
Modular<T> operator-(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) -= rhs;
}

template <typename T, typename U>
Modular<T> operator-(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) -= rhs;
}

template <typename T>
Modular<T> operator*(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}

template <typename T, typename U>
Modular<T> operator*(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) *= rhs;
}

template <typename T, typename U>
Modular<T> operator*(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) *= rhs;
}

template <typename T>
Modular<T> operator/(const Modular<T> &lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}

template <typename T, typename U>
Modular<T> operator/(const Modular<T> &lhs, U rhs) {
  return Modular<T>(lhs) /= rhs;
}

template <typename T, typename U>
Modular<T> operator/(U lhs, const Modular<T> &rhs) {
  return Modular<T>(lhs) /= rhs;
}

template <typename T, typename U>
Modular<T> power(const Modular<T> &a, const U &b) {
  assert(b >= 0);
  Modular<T> x = a, res = 1;
  U p = b;
  while (p > 0) {
    if (p & 1)
      res *= x;
    x *= x;
    p >>= 1;
  }
  return res;
}

template <typename T> bool IsZero(const Modular<T> &number) {
  return number() == 0;
}

template <typename T> string to_string(const Modular<T> &number) {
  return to_string(number());
}

template <typename T>
std::ostream &operator<<(std::ostream &stream, const Modular<T> &number) {
  return stream << number();
}

template <typename T>
std::istream &operator>>(std::istream &stream, Modular<T> &number) {
  typename common_type<typename Modular<T>::Type, int64_t>::type x;
  stream >> x;
  number.value = Modular<T>::normalize(x);
  return stream;
}
constexpr int md = 1000000007;
using Mint = Modular<std::integral_constant<decay<decltype(md)>::type, md>>;
template <typename T> struct Binom {
  vector<T> fact_, inv_fact_;

  explicit Binom(int n) : fact_(n + 1), inv_fact_(n + 1) {
    fact_[0] = 1;
    up(i, 1, n) fact_[i] = fact_[i - 1] * i;
    inv_fact_[n] = 1 / fact_[n];
    down(i, n, 1) { inv_fact_[i - 1] = inv_fact_[i] * i; }
  }

  T binom(int x, int y) const {
    if (x < 0 || y < 0)
      return 0;
    if (x < y)
      return 0;
    assert(x < SZ(fact_));
    return fact_[x] * inv_fact_[y] * inv_fact_[x - y];
  }

  T fact(int n) const {
    assert(n >= 0 && n < SZ(fact_));
    return fact_[n];
  }

  T inv_fact(int n) const {
    assert(n >= 0 && n < SZ(inv_fact_));
    return inv_fact_[n];
  }
};
// debug code by tourist
string to_string(const string &s) { return '"' + s + '"'; }

string to_string(const char *s) { return to_string((string)s); }

string to_string(bool b) { return (b ? "true" : "false"); }

template <typename A, typename B> string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}

template <typename A> string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto &x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}

void debug_out() { cerr << endl; }

template <typename Head, typename... Tail> void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}

#if defined LOCAL && !defined DUIPAI
#define debug(...) cerr << "[" << #__VA_ARGS__ << "]:", debug_out(__VA_ARGS__)
#else
#define debug(...) 42
#endif

int main() {
#if defined LOCAL && !defined DUIPAI
  ifstream in("in.txt");
  cin.rdbuf(in.rdbuf());
#endif
  // a connect subgraph such that number on v is less than number on f[v]
  int n;
  scan(n);
  vv<int> g(n);
  rep(n - 1) {
    int u, v;
    int a, b;
    scan(a, b);
    --a, --b;
    g[a].pb(b);
    g[b].pb(a);
  }
  vector<Mint> a(n, 1), fact(n);
  fact[0] = 1;
  rng(i, 1, n) { fact[i] = fact[i - 1] * i; }
  vi sz(n), fa(n), depth(n);
  function<void(int)> calc = [&](int u) {
    FOR(v, g[u]) {
      if (v != fa[u]) {
        depth[v] = depth[u] + 1;
        fa[v] = u;
        calc(v);
        a[u] *= a[v] / fact[sz[v]];
        sz[u] += sz[v];
      }
    }
    a[u] *= fact[sz[u]];
    sz[u]++;
  };
  calc(0);
  debug(a[0]);
  Binom<Mint> b(n);
  // f(0) = c1 XY
  // f(u) = c2 XY
  // c1 = \binom{n - depth[u], sz[u]}
  // c2 = \binom{n - 1, sz[u] - 1}
  // f(u) = f[0] / c2 * c2
  debug(a);
  debug(depth);
  vector<Mint> ans(n);
  ans[0] = a[0];
  rng(i, 1, n) {
    // 到今天我才明白 rerooting 是什么意思！
    ans[i] = ans[fa[i]] / b.binom(n - 1, sz[i]) * b.binom(n - 1, n - sz[i]);
  }
  rng (i, 0, n) {
    println(ans[i]);
  }
  return 0;
}