Problem p02728 (C++)

Buggy submission (status: Runtime Error):
// includes {{{
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdlib>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <tuple>
#include <vector>
// #include<deque>
// #include<multiset>
// #include<cstring>
// #include<bits/stdc++.h>
// }}}
using namespace std;
using ll = long long;

// #undef DEBUG
// #define DEBUG
// DEBUG {{{
#include <array>
#include <deque>
#include <iostream>
#include <list>
#include <queue>
#include <stack>
#include <tuple>
#include <valarray>
#include <vector>
template <int n, class... T>
typename std::enable_if<(n >= sizeof...(T))>::type
__output_tuple(std::ostream &, std::tuple<T...> const &) {}
template <int n, class... T>
typename std::enable_if<(n < sizeof...(T))>::type
__output_tuple(std::ostream &os, std::tuple<T...> const &t) {
  os << (n == 0 ? "" : ", ") << std::get<n>(t);
  __output_tuple<n + 1>(os, t);
}
template <class... T>
std::ostream &operator<<(std::ostream &os, std::tuple<T...> const &t) {
  os << "(";
  __output_tuple<0>(os, t);
  os << ")";
  return os;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, std::pair<T, U> const &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::stack<T> &a) {
  os << "{";
  for (auto tmp = a; tmp.size(); tmp.pop())
    os << (a.size() == tmp.size() ? "" : ", ") << tmp.top();
  os << "}";
  return os;
}
template <class T, class Container, class Compare>
std::ostream &operator<<(std::ostream &os,
                         std::priority_queue<T, Container, Compare> a) {
  os << "{ (top) ";
  while (a.size())
    os << a.top() << (a.size() == 1 ? "" : ", "), a.pop();
  os << " }";
  return os;
}
template <class T, class Container>
std::ostream &operator<<(std::ostream &os, std::queue<T, Container> a) {
  os << "{ ";
  while (a.size())
    os << a.front() << (a.size() == 1 ? "" : ", "), a.pop();
  os << " }";
  return os;
}
#ifdef DEBUG
#if !defined(DEBUG_OUT)
#define DEBUG_OUT std::cerr
#endif
#define dump(...)                                                              \
  [&]() {                                                                      \
    auto __debug_tap = std::make_tuple(__VA_ARGS__);                           \
    DEBUG_OUT << "[" << __LINE__ << "] " << #__VA_ARGS__ << " = "              \
              << __debug_tap << std::endl;                                     \
  }()
template <class T> inline void dump2D(T &d, size_t sizey, size_t sizex) {
  for (size_t i = 0; i < sizey; i++) {
    DEBUG_OUT << "\t";
    for (size_t j = 0; j < sizex; j++)
      DEBUG_OUT << d[i][j] << (j + 1 == sizex ? "" : "\t");
    DEBUG_OUT << std::endl;
  }
}
template <class T> inline void dump1D(T &d, size_t sizey) {
  for (size_t i = 0; i < sizey; i++) {
    DEBUG_OUT << d[i] << (i + 1 == sizey ? "" : " ");
  }
  DEBUG_OUT << std::endl;
}
template <
    class T,
    class = typename std::iterator_traits<decltype(begin(T()))>::value_type,
    class = typename std::enable_if<!std::is_same<T, std::string>::value>::type>
std::ostream &operator<<(std::ostream &os, const T &a) {
  os << "{";
  for (auto ite = begin(a); ite != end(a); ++ite)
    os << (ite == begin(a) ? "" : ", ") << *ite;
  os << "}";
  return os;
}
#else
#define dump(...) ((void)42)
#define dump2D(...) ((void)42)
#define dump1D(...) ((void)42)
template <
    class T,
    class = typename std::iterator_traits<decltype(begin(T()))>::value_type,
    class = typename std::enable_if<!std::is_same<T, std::string>::value>::type>
std::ostream &operator<<(std::ostream &os, const T &a) {
  for (auto ite = begin(a); ite != end(a); ++ite)
    os << (ite == begin(a) ? "" : " ") << *ite;
  return os;
}
#endif
// }}}

/// --- Modulo Integer {{{ ///
#include <ostream>
template <long long mod = static_cast<long long>(1e9 + 7)>
struct ModuloInteger {
  static_assert(mod > 0, "mod must be positive");
  static_assert(mod <= 3037000499, "mod is too big");
  using integer = long long;
  static ModuloInteger unused;
  // math {{{
  static inline integer extgcd(integer a, integer b, integer &x, integer &y) {
    integer d;
    return b == 0 ? (x = a < 0 ? -1 : 1, y = 0, a < 0 ? -a : a)
                  : (d = extgcd(b, a % b, y, x), y -= a / b * x, d);
  }
  static inline integer modinv(integer a) {
    integer x = 0, y = 0;
    extgcd(a, mod, x, y);
    if (x < 0)
      x += mod;
    else if (x == mod)
      x = 0;
    return x;
  }
  static inline integer modpow(integer a, long long b) {
    if (b < 0)
      b = -b, a = modinv(a);
    integer r = 1;
    a %= mod;
    while (b) {
      if (b & 1)
        r = r * a % mod;
      a = a * a % mod;
      b >>= 1;
    }
    return r;
  }
  // }}}

  integer val;
  constexpr ModuloInteger() : val(0) {}
  constexpr ModuloInteger(integer t) {
    val = t % mod;
    if (val < 0)
      val += mod;
  }

private:
  // strict constructor
  constexpr ModuloInteger(integer t, int) : val(t) {}

public:
  template <class T> explicit operator T() { return T(val); }
  // operator bool() { return bool(val); }
  // ModuloInteger <arithmetic-operator>[=] ModuloInteger {{{
  ModuloInteger operator+(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp += rhs;
    return tmp;
  }
  ModuloInteger operator-(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp -= rhs;
    return tmp;
  }
  ModuloInteger operator*(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp *= rhs;
    return tmp;
  }
  ModuloInteger operator/(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp /= rhs;
    return tmp;
  }
  ModuloInteger &operator+=(ModuloInteger const &rhs) {
    val = val + rhs.val;
    if (val >= mod)
      val -= mod;
    return *this;
  }
  ModuloInteger &operator-=(ModuloInteger const &rhs) { return *this += -rhs; }
  ModuloInteger &operator*=(ModuloInteger const &rhs) {
    val = val * rhs.val % mod;
    return *this;
  }
  ModuloInteger &operator/=(ModuloInteger const &rhs) {
    return *this *= rhs.inv();
  }
  // }}}
  // increment, decrement {{{
  ModuloInteger operator++(int) {
    ModuloInteger tmp = *this;
    val = val + 1;
    if (val >= mod)
      val = 0;
    return tmp;
  }
  ModuloInteger operator--(int) {
    ModuloInteger tmp = *this;
    val = val == 0 ? mod - 1 : val - 1;
    return tmp;
  }
  ModuloInteger &operator++() {
    val = val + 1;
    if (val >= mod)
      val = 0;
    return *this;
  }
  ModuloInteger &operator--() {
    val = val == 0 ? mod - 1 : val - 1;
    return *this;
  }
  // }}}
  ModuloInteger operator-() const {
    return ModuloInteger(val == 0 ? 0 : mod - val, 0);
  }
  // ModuloInteger <arithmetic-operator>[=] T {{{
  template <typename T> ModuloInteger operator+(T const &rhs) const {
    return ModuloInteger(val + rhs % mod);
  }
  template <typename T> ModuloInteger operator-(T const &rhs) const {
    return ModuloInteger(mod + val - rhs % mod);
  }
  template <typename T> ModuloInteger operator*(T const &rhs) const {
    return ModuloInteger(val * (rhs % mod));
  }
  template <typename T> ModuloInteger operator/(T const &rhs) const {
    return ModuloInteger(val * modinv(rhs));
  }
  template <typename T> ModuloInteger &operator+=(T const &rhs) {
    val = (mod + val + rhs % mod) % mod;
    return *this;
  }
  template <typename T> ModuloInteger &operator-=(T const &rhs) {
    val = (mod + val - rhs % mod) % mod;
    return *this;
  }
  template <typename T> ModuloInteger &operator*=(T const &rhs) {
    val = val * (mod + rhs % mod) % mod;
    return *this;
  }
  template <typename T> ModuloInteger &operator/=(T const &rhs) {
    val = val * modinv(rhs) % mod;
    return *this;
  }
  // }}}
  ModuloInteger inv() const { return ModuloInteger(modinv(val), 0); }
  ModuloInteger operator~() const { return inv(); }
  friend std::ostream &operator<<(std::ostream &os, ModuloInteger const &mv) {
    os << mv.val;
    return os;
  }
  // equality operator {{{
  ModuloInteger operator==(const ModuloInteger &a) const {
    return val == a.val;
  }
  ModuloInteger operator!=(const ModuloInteger &a) const {
    return val != a.val;
  }
  ModuloInteger operator==(const integer &a) const {
    return val == ModuloInteger(a);
  }
  ModuloInteger operator!=(const integer &a) const {
    return val != ModuloInteger(a);
  }
  // }}}
  // T <arithmetic-operator> ModuloInteger {{{
  friend constexpr ModuloInteger operator+(integer a, ModuloInteger const &mv) {
    return ModuloInteger(a % mod + mv.val);
  }
  friend constexpr ModuloInteger operator-(integer a, ModuloInteger const &mv) {
    return ModuloInteger(a % mod - mv.val);
  }
  friend constexpr ModuloInteger operator*(integer a, ModuloInteger const &mv) {
    return ModuloInteger((mod + a % mod) * mv.val % mod, 0);
  }
  friend constexpr ModuloInteger operator/(integer a, ModuloInteger const &mv) {
    return ModuloInteger((mod + a % mod) * modinv(mv.val) % mod, 0);
  }
  // }}}
  // power {{{
  ModuloInteger operator^(integer x) const { return pow(*this, x); }
  ModuloInteger &operator^=(integer x) {
    val = modpow(val, x);
    return *this;
  }
  friend ModuloInteger pow(ModuloInteger x, integer y) {
    return ModuloInteger(modpow(x.val, y), 0);
  }
  // }}}
};
template <long long mod> ModuloInteger<mod> ModuloInteger<mod>::unused(mod, 0);
/// }}}--- ///

using modint = ModuloInteger<>;

// NOTE : use H with larger N
/// --- Modulo Factorial {{{ ///
#include <cassert>
#include <cstddef>
template <std::size_t N, int mod = static_cast<int>(1e9 + 7)> struct Factorial {
  using integer = long long;
  constexpr integer extgcd(integer a, integer b, integer &x, integer &y) {
    integer d = 0;
    return b == 0 ? (x = a < 0 ? -1 : 1, y = 0, a < 0 ? -a : a)
                  : (d = extgcd(b, a % b, y, x), y -= a / b * x, d);
  }
  constexpr integer modinv(integer a) {
    integer x = 0, y = 0;
    extgcd(a, mod, x, y);
    if (x < 0)
      x += mod;
    else if (x == mod)
      x = 0;
    return x;
  }
  int arr[N + 1], inv[N + 1];
  integer operator[](int i) const { return arr[i]; }
  Factorial() : arr(), inv() {
    arr[0] = 1;
    for (std::size_t i = 1; i <= N; i++) {
      arr[i] = (integer)i * arr[i - 1] % mod;
    }
    inv[N] = modinv(arr[N]);
    for (int i = N - 1; i >= 0; i--) {
      inv[i] = (integer)(i + 1) * inv[i + 1] % mod;
    }
  }
  integer C(int n, int r) const {
    if (n < 0 || r < 0 || n < r)
      return 0;
    assert(n <= N);
    return (integer)arr[n] * inv[r] % mod * inv[n - r] % mod;
  }
  integer H(int n, int r) const { return C(n + r - 1, r); }
};
/// }}}--- ///

constexpr int mod = 1e9 + 7;
const int N = 1e5 + 10;
Factorial<N * 2, mod> fact;

vector<vector<int>> g(N);
using Value = tuple<int, modint, modint>; // sum, rev-sum
map<int, Value> dp[N];
Value dfs(int i, int p, int f) {
  if (dp[i].count(p))
    return dp[i][p];
  int deg = g[i].size() - (p != -1);
  Value res = Value(0, 1, 1);
  if (f || p == -1) {
    // O(deg)
    // go only child
    for (int j : g[i])
      if (j != p) {
        int k;
        modint x, y;
        tie(k, x, y) = dfs(j, i, f);
        get<0>(res) += k;
        get<1>(res) *= fact.inv[k];
        get<2>(res) *= y;
      }
    get<2>(res) *= fact[get<0>(res)] * get<1>(res);
    get<0>(res) += 1;
  } else {
    // O(1)
    auto A = dfs(i, -1, f), B = dfs(p, i, f);
    res = Value(get<0>(A) - get<0>(B), get<1>(A) * fact[get<0>(B)],
                get<2>(A) / fact[get<0>(A) - 1] *
                    fact[get<0>(A) - 1 - get<0>(B)] * fact[get<0>(B)] /
                    get<2>(B));
    dump(A);
    dump(B);
    dump(0, i, p, res);
  }
  return dp[i][p] = res;
}

int n;
int main() {
  std::ios::sync_with_stdio(false), std::cin.tie(0);
  cin >> n;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    g[a].emplace_back(b);
    g[b].emplace_back(a);
  }
  dfs(0, -1, 1);
  for (int i = 0; i < n; i++) {
    auto A = dfs(i, -1, 0);
    dump(A);
    cout << get<2>(A) << "\n";
  }
  return 0;
}


Fixed submission:
// includes {{{
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <cstdlib>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <tuple>
#include <vector>
// #include<deque>
// #include<multiset>
// #include<cstring>
// #include<bits/stdc++.h>
// }}}
using namespace std;
using ll = long long;

// #undef DEBUG
// #define DEBUG
// DEBUG {{{
#include <array>
#include <deque>
#include <iostream>
#include <list>
#include <queue>
#include <stack>
#include <tuple>
#include <valarray>
#include <vector>
template <int n, class... T>
typename std::enable_if<(n >= sizeof...(T))>::type
__output_tuple(std::ostream &, std::tuple<T...> const &) {}
template <int n, class... T>
typename std::enable_if<(n < sizeof...(T))>::type
__output_tuple(std::ostream &os, std::tuple<T...> const &t) {
  os << (n == 0 ? "" : ", ") << std::get<n>(t);
  __output_tuple<n + 1>(os, t);
}
template <class... T>
std::ostream &operator<<(std::ostream &os, std::tuple<T...> const &t) {
  os << "(";
  __output_tuple<0>(os, t);
  os << ")";
  return os;
}
template <class T, class U>
std::ostream &operator<<(std::ostream &os, std::pair<T, U> const &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <class T>
std::ostream &operator<<(std::ostream &os, const std::stack<T> &a) {
  os << "{";
  for (auto tmp = a; tmp.size(); tmp.pop())
    os << (a.size() == tmp.size() ? "" : ", ") << tmp.top();
  os << "}";
  return os;
}
template <class T, class Container, class Compare>
std::ostream &operator<<(std::ostream &os,
                         std::priority_queue<T, Container, Compare> a) {
  os << "{ (top) ";
  while (a.size())
    os << a.top() << (a.size() == 1 ? "" : ", "), a.pop();
  os << " }";
  return os;
}
template <class T, class Container>
std::ostream &operator<<(std::ostream &os, std::queue<T, Container> a) {
  os << "{ ";
  while (a.size())
    os << a.front() << (a.size() == 1 ? "" : ", "), a.pop();
  os << " }";
  return os;
}
#ifdef DEBUG
#if !defined(DEBUG_OUT)
#define DEBUG_OUT std::cerr
#endif
#define dump(...)                                                              \
  [&]() {                                                                      \
    auto __debug_tap = std::make_tuple(__VA_ARGS__);                           \
    DEBUG_OUT << "[" << __LINE__ << "] " << #__VA_ARGS__ << " = "              \
              << __debug_tap << std::endl;                                     \
  }()
template <class T> inline void dump2D(T &d, size_t sizey, size_t sizex) {
  for (size_t i = 0; i < sizey; i++) {
    DEBUG_OUT << "\t";
    for (size_t j = 0; j < sizex; j++)
      DEBUG_OUT << d[i][j] << (j + 1 == sizex ? "" : "\t");
    DEBUG_OUT << std::endl;
  }
}
template <class T> inline void dump1D(T &d, size_t sizey) {
  for (size_t i = 0; i < sizey; i++) {
    DEBUG_OUT << d[i] << (i + 1 == sizey ? "" : " ");
  }
  DEBUG_OUT << std::endl;
}
template <
    class T,
    class = typename std::iterator_traits<decltype(begin(T()))>::value_type,
    class = typename std::enable_if<!std::is_same<T, std::string>::value>::type>
std::ostream &operator<<(std::ostream &os, const T &a) {
  os << "{";
  for (auto ite = begin(a); ite != end(a); ++ite)
    os << (ite == begin(a) ? "" : ", ") << *ite;
  os << "}";
  return os;
}
#else
#define dump(...) ((void)42)
#define dump2D(...) ((void)42)
#define dump1D(...) ((void)42)
template <
    class T,
    class = typename std::iterator_traits<decltype(begin(T()))>::value_type,
    class = typename std::enable_if<!std::is_same<T, std::string>::value>::type>
std::ostream &operator<<(std::ostream &os, const T &a) {
  for (auto ite = begin(a); ite != end(a); ++ite)
    os << (ite == begin(a) ? "" : " ") << *ite;
  return os;
}
#endif
// }}}

/// --- Modulo Integer {{{ ///
#include <ostream>
template <long long mod = static_cast<long long>(1e9 + 7)>
struct ModuloInteger {
  static_assert(mod > 0, "mod must be positive");
  static_assert(mod <= 3037000499, "mod is too big");
  using integer = long long;
  static ModuloInteger unused;
  // math {{{
  static inline integer extgcd(integer a, integer b, integer &x, integer &y) {
    integer d;
    return b == 0 ? (x = a < 0 ? -1 : 1, y = 0, a < 0 ? -a : a)
                  : (d = extgcd(b, a % b, y, x), y -= a / b * x, d);
  }
  static inline integer modinv(integer a) {
    integer x = 0, y = 0;
    extgcd(a, mod, x, y);
    if (x < 0)
      x += mod;
    else if (x == mod)
      x = 0;
    return x;
  }
  static inline integer modpow(integer a, long long b) {
    if (b < 0)
      b = -b, a = modinv(a);
    integer r = 1;
    a %= mod;
    while (b) {
      if (b & 1)
        r = r * a % mod;
      a = a * a % mod;
      b >>= 1;
    }
    return r;
  }
  // }}}

  integer val;
  constexpr ModuloInteger() : val(0) {}
  constexpr ModuloInteger(integer t) {
    val = t % mod;
    if (val < 0)
      val += mod;
  }

private:
  // strict constructor
  constexpr ModuloInteger(integer t, int) : val(t) {}

public:
  template <class T> explicit operator T() { return T(val); }
  // operator bool() { return bool(val); }
  // ModuloInteger <arithmetic-operator>[=] ModuloInteger {{{
  ModuloInteger operator+(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp += rhs;
    return tmp;
  }
  ModuloInteger operator-(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp -= rhs;
    return tmp;
  }
  ModuloInteger operator*(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp *= rhs;
    return tmp;
  }
  ModuloInteger operator/(ModuloInteger const &rhs) const {
    ModuloInteger tmp = *this;
    tmp /= rhs;
    return tmp;
  }
  ModuloInteger &operator+=(ModuloInteger const &rhs) {
    val = val + rhs.val;
    if (val >= mod)
      val -= mod;
    return *this;
  }
  ModuloInteger &operator-=(ModuloInteger const &rhs) { return *this += -rhs; }
  ModuloInteger &operator*=(ModuloInteger const &rhs) {
    val = val * rhs.val % mod;
    return *this;
  }
  ModuloInteger &operator/=(ModuloInteger const &rhs) {
    return *this *= rhs.inv();
  }
  // }}}
  // increment, decrement {{{
  ModuloInteger operator++(int) {
    ModuloInteger tmp = *this;
    val = val + 1;
    if (val >= mod)
      val = 0;
    return tmp;
  }
  ModuloInteger operator--(int) {
    ModuloInteger tmp = *this;
    val = val == 0 ? mod - 1 : val - 1;
    return tmp;
  }
  ModuloInteger &operator++() {
    val = val + 1;
    if (val >= mod)
      val = 0;
    return *this;
  }
  ModuloInteger &operator--() {
    val = val == 0 ? mod - 1 : val - 1;
    return *this;
  }
  // }}}
  ModuloInteger operator-() const {
    return ModuloInteger(val == 0 ? 0 : mod - val, 0);
  }
  // ModuloInteger <arithmetic-operator>[=] T {{{
  template <typename T> ModuloInteger operator+(T const &rhs) const {
    return ModuloInteger(val + rhs % mod);
  }
  template <typename T> ModuloInteger operator-(T const &rhs) const {
    return ModuloInteger(mod + val - rhs % mod);
  }
  template <typename T> ModuloInteger operator*(T const &rhs) const {
    return ModuloInteger(val * (rhs % mod));
  }
  template <typename T> ModuloInteger operator/(T const &rhs) const {
    return ModuloInteger(val * modinv(rhs));
  }
  template <typename T> ModuloInteger &operator+=(T const &rhs) {
    val = (mod + val + rhs % mod) % mod;
    return *this;
  }
  template <typename T> ModuloInteger &operator-=(T const &rhs) {
    val = (mod + val - rhs % mod) % mod;
    return *this;
  }
  template <typename T> ModuloInteger &operator*=(T const &rhs) {
    val = val * (mod + rhs % mod) % mod;
    return *this;
  }
  template <typename T> ModuloInteger &operator/=(T const &rhs) {
    val = val * modinv(rhs) % mod;
    return *this;
  }
  // }}}
  ModuloInteger inv() const { return ModuloInteger(modinv(val), 0); }
  ModuloInteger operator~() const { return inv(); }
  friend std::ostream &operator<<(std::ostream &os, ModuloInteger const &mv) {
    os << mv.val;
    return os;
  }
  // equality operator {{{
  ModuloInteger operator==(const ModuloInteger &a) const {
    return val == a.val;
  }
  ModuloInteger operator!=(const ModuloInteger &a) const {
    return val != a.val;
  }
  ModuloInteger operator==(const integer &a) const {
    return val == ModuloInteger(a);
  }
  ModuloInteger operator!=(const integer &a) const {
    return val != ModuloInteger(a);
  }
  // }}}
  // T <arithmetic-operator> ModuloInteger {{{
  friend constexpr ModuloInteger operator+(integer a, ModuloInteger const &mv) {
    return ModuloInteger(a % mod + mv.val);
  }
  friend constexpr ModuloInteger operator-(integer a, ModuloInteger const &mv) {
    return ModuloInteger(a % mod - mv.val);
  }
  friend constexpr ModuloInteger operator*(integer a, ModuloInteger const &mv) {
    return ModuloInteger((mod + a % mod) * mv.val % mod, 0);
  }
  friend constexpr ModuloInteger operator/(integer a, ModuloInteger const &mv) {
    return ModuloInteger((mod + a % mod) * modinv(mv.val) % mod, 0);
  }
  // }}}
  // power {{{
  ModuloInteger operator^(integer x) const { return pow(*this, x); }
  ModuloInteger &operator^=(integer x) {
    val = modpow(val, x);
    return *this;
  }
  friend ModuloInteger pow(ModuloInteger x, integer y) {
    return ModuloInteger(modpow(x.val, y), 0);
  }
  // }}}
};
template <long long mod> ModuloInteger<mod> ModuloInteger<mod>::unused(mod, 0);
/// }}}--- ///

using modint = ModuloInteger<>;

// NOTE : use H with larger N
/// --- Modulo Factorial {{{ ///
#include <cassert>
#include <cstddef>
template <std::size_t N, int mod = static_cast<int>(1e9 + 7)> struct Factorial {
  using integer = long long;
  constexpr integer extgcd(integer a, integer b, integer &x, integer &y) {
    integer d = 0;
    return b == 0 ? (x = a < 0 ? -1 : 1, y = 0, a < 0 ? -a : a)
                  : (d = extgcd(b, a % b, y, x), y -= a / b * x, d);
  }
  constexpr integer modinv(integer a) {
    integer x = 0, y = 0;
    extgcd(a, mod, x, y);
    if (x < 0)
      x += mod;
    else if (x == mod)
      x = 0;
    return x;
  }
  int arr[N + 1], inv[N + 1];
  integer operator[](int i) const { return arr[i]; }
  Factorial() : arr(), inv() {
    arr[0] = 1;
    for (std::size_t i = 1; i <= N; i++) {
      arr[i] = (integer)i * arr[i - 1] % mod;
    }
    inv[N] = modinv(arr[N]);
    for (int i = N - 1; i >= 0; i--) {
      inv[i] = (integer)(i + 1) * inv[i + 1] % mod;
    }
  }
  integer C(int n, int r) const {
    if (n < 0 || r < 0 || n < r)
      return 0;
    assert(n <= N);
    return (integer)arr[n] * inv[r] % mod * inv[n - r] % mod;
  }
  integer H(int n, int r) const { return C(n + r - 1, r); }
};
/// }}}--- ///

constexpr int mod = 1e9 + 7;
const int N = 2e5 + 10;
Factorial<N * 2, mod> fact;

vector<vector<int>> g(N);
using Value = tuple<int, modint, modint>; // sum, rev-sum
map<int, Value> dp[N];
Value dfs(int i, int p, int f) {
  if (dp[i].count(p))
    return dp[i][p];
  int deg = g[i].size() - (p != -1);
  Value res = Value(0, 1, 1);
  if (f || p == -1) {
    // O(deg)
    // go only child
    for (int j : g[i])
      if (j != p) {
        int k;
        modint x, y;
        tie(k, x, y) = dfs(j, i, f);
        get<0>(res) += k;
        get<1>(res) *= fact.inv[k];
        get<2>(res) *= y;
      }
    get<2>(res) *= fact[get<0>(res)] * get<1>(res);
    get<0>(res) += 1;
  } else {
    // O(1)
    auto A = dfs(i, -1, f), B = dfs(p, i, f);
    res = Value(get<0>(A) - get<0>(B), get<1>(A) * fact[get<0>(B)],
                get<2>(A) / fact[get<0>(A) - 1] *
                    fact[get<0>(A) - 1 - get<0>(B)] * fact[get<0>(B)] /
                    get<2>(B));
    dump(A);
    dump(B);
    dump(0, i, p, res);
  }
  return dp[i][p] = res;
}

int n;
int main() {
  std::ios::sync_with_stdio(false), std::cin.tie(0);
  cin >> n;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    g[a].emplace_back(b);
    g[b].emplace_back(a);
  }
  dfs(0, -1, 1);
  for (int i = 0; i < n; i++) {
    auto A = dfs(i, -1, 0);
    dump(A);
    cout << get<2>(A) << "\n";
  }
  return 0;
}