You are given a tree (an undirected connected graph without cycles) and an integer s.

Vanya wants to put weights on all edges of the tree so that all weights are non-negative real numbers and their sum is s. At the same time, he wants to make the diameter of the tree as small as possible.

Let's define the diameter of a weighed tree as the maximum sum of the weights of the edges lying on the path between two some vertices of the tree. In other words, the diameter of a weighed tree is the length of the longest simple path in the tree, where length of a path is equal to the sum of weights over all edges in the path.

Find the minimum possible diameter that Vanya can get.

Input

The first line contains two integer numbers n and s (2 ≤ n ≤ 10^5, 1 ≤ s ≤ 10^9) — the number of vertices in the tree and the sum of edge weights.

Each of the following n−1 lines contains two space-separated integer numbers a_i and b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i) — the indexes of vertices connected by an edge. The edges are undirected.

It is guaranteed that the given edges form a tree.

Output

Print the minimum diameter of the tree that Vanya can get by placing some non-negative real weights on its edges with the sum equal to s.

Your answer will be considered correct if its absolute or relative error does not exceed 10^{-6}.

Formally, let your answer be a, and the jury's answer be b. Your answer is considered correct if \frac {|a-b|} {max(1, b)} ≤ 10^{-6}.

Examples

Input


4 3
1 2
1 3
1 4


Output


2.000000000000000000

Input


6 1
2 1
2 3
2 5
5 4
5 6


Output


0.500000000000000000

Input


5 5
1 2
2 3
3 4
3 5


Output


3.333333333333333333

Note

In the first example it is necessary to put weights like this:

<image>

It is easy to see that the diameter of this tree is 2. It can be proved that it is the minimum possible diameter.

In the second example it is necessary to put weights like this:

<image>
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1e9 + 7;
using ll = long long;
using ld = long double;
using db = long double;
using str = string;
using pi = pair<int, int>;
using pl = pair<ll, ll>;
using pd = pair<double, double>;
using vi = vector<int>;
using vb = vector<bool>;
using vl = vector<ll>;
using vd = vector<double>;
using vs = vector<string>;
using vpi = vector<pi>;
using vpl = vector<pl>;
using vpd = vector<pd>;
template <typename A, typename B>
pair<A, B>& operator++(pair<A, B>& a) {
  ++a.second;
  ++a.first;
  return a;
}
template <typename A, typename B>
pair<A, B>& operator--(pair<A, B>& a) {
  --a.first;
  --a.second;
  return a;
}
template <typename A>
vector<A>& operator++(vector<A>& a) {
  for (auto it = a.begin(); it != a.end(); ++it) ++*it;
  return a;
}
template <typename A>
vector<A>& operator--(vector<A>& a) {
  for (auto it = a.begin(); it != a.end(); ++it) --*it;
  return a;
}
const int di[4] = {-1, 0, 1, 0}, dj[4] = {0, 1, 0, -1};
const int di8[8] = {-1, -1, 0, 1, 1, 1, 0, -1},
          dj8[8] = {0, 1, 1, 1, 0, -1, -1, -1};
const ld PI = acos((ld)-1);
const ll INF = 1e18;
const double eps = 1e-11;
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
ll randint(ll a, ll b) { return uniform_int_distribution<ll>(a, b)(rng); }
using ul = unsigned long long;
ul modMul(ul a, ul b, const ul mod) {
  ll ret = a * b - mod * (ul)((ld)a * b / mod);
  return ret + ((ret < 0) - (ret >= (ll)mod)) * mod;
}
ul modPow(ul a, ul b, const ul mod) {
  if (b == 0) return 1;
  ul res = modPow(a, b / 2, mod);
  res = modMul(res, res, mod);
  return b & 1 ? modMul(res, a, mod) : res;
}
bool pow2(int i) { return i && (i & -i) == i; }
constexpr int pct(int x) { return __builtin_popcount(x); }
constexpr int bits(int x) { return 31 - __builtin_clz(x); }
ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); }
ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); }
ll half(ll x) { return fdiv(x, 2); }
bool inc(ll a, ll b, ll c) { return a <= b && b <= c; }
template <class t>
int lwb(const vector<t>& v, const t& a) {
  return lower_bound((v).begin(), (v).end(), a) - v.begin();
}
template <class T>
bool chmin(T& a, const T& b) {
  return b < a ? a = b, 1 : 0;
}
template <class T>
bool chmax(T& a, const T& b) {
  return a < b ? a = b, 1 : 0;
}
void TIME() {}
template <class T>
void remDup(vector<T>& v) {
  sort((v).begin(), (v).end());
  v.erase(unique((v).begin(), (v).end()), end(v));
}
template <class T, class U>
void remAll(vector<T>& v, U a) {
  v.erase(remove((v).begin(), (v).end(), a), v.end());
}
template <class T, class U>
T fstTrue(T lo, T hi, U f) {
  while (lo < hi) {
    T mid = half(lo + hi);
    f(mid) ? hi = mid : lo = mid + 1;
  }
  return lo;
}
template <class T, class U>
T lstTrue(T lo, T hi, U f) {
  while (lo < hi) {
    T mid = half(lo + hi + 1);
    f(mid) ? lo = mid : hi = mid - 1;
  }
  return lo;
}
template <typename I>
struct _reversed_struct {
  I& v_;
  explicit _reversed_struct(I& v) : v_{v} {}
  typename I::reverse_iterator begin() const { return v_.rbegin(); }
  typename I::reverse_iterator end() const { return v_.rend(); }
};
template <typename I>
_reversed_struct<I> reversed(I& v) {
  return _reversed_struct<I>(v);
}
string to_string(char c) { return string(1, c); }
string to_string(bool b) { return to_string((int)b); }
string to_string(const char* s) { return (string)s; }
string to_string(string s) { return s; }
template <class T>
string to_string(complex<T> c) {
  stringstream ss;
  ss << c;
  return ss.str();
}
string to_string(vb v) {
  string res = "{";
  for (int i = (0); i < (((int)(v).size())); ++i) res += char('0' + v[i]);
  res += "}";
  return res;
}
template <size_t SZ>
string to_string(bitset<SZ> b) {
  string res = "";
  for (int i = (0); i < (((int)(b).size())); ++i) res += char('0' + b[i]);
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p);
template <class T>
string to_string(T v) {
  bool fst = 1;
  string res = "";
  for (const auto& x : v) {
    if (!fst) res += " ";
    fst = 0;
    res += to_string(x);
  }
  return res;
}
template <class T, class U>
string to_string(pair<T, U> p) {
  return to_string(p.first) + " " + to_string(p.second);
}
template <class T>
void re(complex<T>& c);
template <class T, class U>
void re(pair<T, U>& p);
template <class T>
void re(vector<T>& v);
template <class T>
void rv(int n, vector<T>& x) {
  x.resize(n);
  re(x);
}
template <class T, size_t SZ>
void re(array<T, SZ>& a);
template <class T>
void re(T& x) {
  cin >> x;
}
void re(double& d) {
  string t;
  re(t);
  d = stod(t);
}
void re(ld& d) {
  string t;
  re(t);
  d = stold(t);
}
template <class T, class... U>
void re(T& t, U&... u) {
  re(t);
  re(u...);
}
template <class T>
void re(complex<T>& c) {
  T a, b;
  re(a, b);
  c = {a, b};
}
template <class T, class U>
void re(pair<T, U>& p) {
  re(p.first, p.second);
}
template <class T>
void re(vector<T>& x) {
  for (auto& a : x) re(a);
}
template <class T, size_t SZ>
void re(array<T, SZ>& x) {
  for (auto& a : x) re(a);
}
template <class T>
void pr(T x) {
  cout << to_string(x);
}
template <class T, class... U>
void pr(const T& t, const U&... u) {
  pr(t);
  pr(u...);
}
void ps() { pr("\n"); }
template <class T, class... U>
void ps(const T& t, const U&... u) {
  pr(t);
  if (sizeof...(u)) pr(" ");
  ps(u...);
}
struct chash {
  static uint64_t splitmix64(uint64_t x) {
    x += 0x9e3779b97f4a7c15;
    x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
    x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
    return x ^ (x >> 31);
  }
  size_t operator()(uint64_t x) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(x + FIXED_RANDOM);
  }
  template <typename L, typename R>
  size_t operator()(pair<L, R> const& Y) const {
    static const uint64_t FIXED_RANDOM =
        chrono::steady_clock::now().time_since_epoch().count();
    return splitmix64(Y.first * 31 + Y.second + FIXED_RANDOM);
  }
};
template <class T>
using V = vector<T>;
template <class T, size_t SZ>
using AR = array<T, SZ>;
template <class T>
using mpq = priority_queue<T, vector<T>, greater<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using ms = multiset<T>;
template <class T, class U>
using um = unordered_map<T, U, chash>;
template <class T>
using us = unordered_set<T, chash>;
template <class T>
using PR = pair<T, T>;
template <int MOD, int RT>
struct mint {
  static const int mod = MOD;
  static constexpr mint rt() { return RT; }
  int v;
  explicit operator int() const { return v; }
  mint() { v = 0; }
  mint(ll _v) {
    v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
    if (v < 0) v += MOD;
  }
  friend bool operator==(const mint& a, const mint& b) { return a.v == b.v; }
  friend bool operator!=(const mint& a, const mint& b) { return !(a == b); }
  friend bool operator<(const mint& a, const mint& b) { return a.v < b.v; }
  friend void re(mint& a) {
    ll x;
    re(x);
    a = mint(x);
  }
  friend string to_string(mint a) { return to_string(a.v); }
  mint& operator+=(const mint& m) {
    if ((v += m.v) >= MOD) v -= MOD;
    return *this;
  }
  mint& operator-=(const mint& m) {
    if ((v -= m.v) < 0) v += MOD;
    return *this;
  }
  mint& operator*=(const mint& m) {
    v = (ll)v * m.v % MOD;
    return *this;
  }
  mint& operator/=(const mint& m) { return (*this) *= inv(m); }
  friend mint pow(mint a, ll p) {
    mint ans = 1;
    assert(p >= 0);
    for (; p; p /= 2, a *= a)
      if (p & 1) ans *= a;
    return ans;
  }
  friend mint inv(const mint& a) {
    assert(a.v != 0);
    return pow(a, MOD - 2);
  }
  mint operator-() const { return mint(-v); }
  mint& operator++() { return *this += 1; }
  mint& operator--() { return *this -= 1; }
  friend mint operator+(mint a, const mint& b) { return a += b; }
  friend mint operator-(mint a, const mint& b) { return a -= b; }
  friend mint operator*(mint a, const mint& b) { return a *= b; }
  friend mint operator/(mint a, const mint& b) { return a /= b; }
};
typedef mint<MOD, 5> mi;
vi invs, fac, ifac;
void genFac(int SZ) {
  invs.resize(SZ), fac.resize(SZ), ifac.resize(SZ);
  invs[1] = fac[0] = ifac[0] = 1;
  for (int i = (2); i < (SZ); ++i)
    invs[i] = MOD - (ll)MOD / i * invs[MOD % i] % MOD;
  for (int i = (1); i < (SZ); ++i) {
    fac[i] = (ll)fac[i - 1] * i % MOD;
    ifac[i] = (ll)ifac[i - 1] * invs[i] % MOD;
  }
}
mi comb(int a, int b) {
  if (a < b || b < 0) return 0;
  return (ll)fac[a] * ifac[b] % MOD * ifac[a - b] % MOD;
}
ll gcd(ll a, ll b) { return b ? gcd(b, a % b) : a; }
ll lcm(ll a, ll b) { return (a / gcd(a, b)) * b; }
ll ncr(ll a, ll b) {
  if (a < b) return 0;
  ll f = 1;
  for (int i = (1); i < (b + 1); ++i) {
    f *= (a + 1 - i);
    f /= i;
  }
  return f;
}
void DBG() { cerr << "]" << endl; }
template <class T, class... U>
void DBG(const T& t, const U&... u) {
  cerr << to_string(t);
  if (sizeof...(u)) cerr << ", ";
  DBG(u...);
}
V<vi> reg(int n, int m) {
  V<vi> g(n);
  for (int i = (0); i < (m); ++i) {
    int a, b;
    re(a, b);
    a--;
    b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  return g;
}
V<vpi> rew(int n, int m) {
  V<vpi> g(n);
  for (int i = (0); i < (m); ++i) {
    int a, b, w;
    re(a, b, w);
    a--;
    b--;
    g[a].emplace_back(b, w);
    g[b].emplace_back(a, w);
  }
  return g;
}
void setPrec() { cout << fixed << setprecision(15); }
void setIn(str s) { freopen(s.c_str(), "r", stdin); }
void setOut(str s) { freopen(s.c_str(), "w", stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str s = "") {
  unsyncIO();
  setPrec();
  if (((int)(s).size())) {
    setIn(s + ".in");
    setOut(s + ".out");
  }
}
const int N = 2e5 + 5;
int n, s;
V<vi> adj;
void solve(int tc) {
  int n, m, l = 0;
  re(n, s);
  adj = reg(n, n - 1);
  for (int i = (0); i < (n); ++i) l += ((int)(adj[i]).size()) == 1;
  cout << (db)2.0 * s / l;
}
int main() {
  setIO();
  int T = 1;
  for (int _ = (1); _ < (T + 1); ++_) solve(_);
}
