#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
void print(ll x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes" << endl;
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No" << endl;
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible" << endl;
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible" << endl;
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
ll mask(ll i) { return (ll(1) << i) - 1; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static random_device rd;
  static mt19937_64 gen(rd());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
ll lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
template <class E>
struct cactus {
  const vvc<E>& g;
  const ll n;
  vvc<ll> cs;
  vi vis, par, u;
  void dfs(ll v, ll p) {
    assert(vis[v] == 0);
    vis[v] = 1;
    par[v] = p;
    for (ll to : g[v])
      if (to != p) {
        if (vis[to] == 0)
          dfs(to, v);
        else if (vis[to] == 1) {
          ll x = v;
          vi z{x};
          while (x != to) {
            x = par[x];
            z.push_back(x);
          }
          cs.push_back(z);
        }
      }
    vis[v] = 2;
  }
  cactus(const vvc<E>& gg) : g(gg), n(g.size()), vis(n), par(n), u(n) {
    for (ll i = ll(0); i < ll(n); i++)
      if (!vis[i]) dfs(i, -1);
  }
};
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  ll n, m;
  cin >> n >> m;
  vc<map<ll, ll>> id(n);
  vvc<ll> g(n);
  vc<pi> es;
  for (ll i = ll(0); i < ll(m); i++) {
    ll first, second;
    cin >> first >> second;
    first--;
    second--;
    id[first][second] = id[second][first] = i;
    g[first].push_back(second);
    g[second].push_back(first);
    es.emplace_back(first, second);
  }
  auto cs = cactus<ll>(g).cs;
  void(0);
  vi src(m, -1), val(m);
  for (auto c : cs)
    if (c.size() > 2) {
      ll s = c.size();
      vi d(s);
      for (ll i = ll(0); i < ll(s); i++) d[i] = id[c[i]][c[(i + 1) % s]];
      ll p = min_element(d.begin(), d.end()) - d.begin();
      ll q = max_element(d.begin(), d.end()) - d.begin();
      bool ok = true;
      for (ll i = p; i != q;) {
        ll j = (i + 1) % s;
        if (d[i] > d[j]) ok = false;
        i = j;
      }
      for (ll i = q; i != p;) {
        ll j = (i + 1) % s;
        if (d[i] < d[j]) ok = false;
        i = j;
      }
      if (ok) {
        src[d[p]] = d[q];
      }
    }
  vi cnt(n, 1);
  for (ll i = ll(m) - 1; i >= ll(0); i--) {
    ll first, second;
    tie(first, second) = es[i];
    cnt[first] = cnt[second] = val[i] = cnt[first] + cnt[second];
    if (src[i] != -1) {
      cnt[first] -= val[src[i]];
      cnt[second] -= val[src[i]];
    }
  }
  for (ll i = ll(0); i < ll(n); i++) cnt[i]--;
  print(cnt);
}

### Prompt

Your task is to create a cpp solution to the following problem:

You are given a cactus graph, in this graph each edge lies on at most one simple cycle.

It is given as m edges a_i, b_i, weight of i-th edge is i.

Let's call a path in cactus increasing if the weights of edges on this path are increasing.

Let's call a pair of vertices (u,v) happy if there exists an increasing path that starts in u and ends in v.

For each vertex u find the number of other vertices v, such that pair (u,v) is happy.

Input

The first line of input contains two integers n,m (1 ≤ n, m ≤ 500 000): the number of vertices and edges in the given cactus.

The next m lines contain a description of cactus edges, i-th of them contain two integers a_i, b_i (1 ≤ a_i, b_i ≤ n, a_i ≠ b_i).

It is guaranteed that there are no multiple edges and the graph is connected.

Output

Print n integers, required values for vertices 1,2,…,n.

Examples

Input


3 3
1 2
2 3
3 1


Output


2 2 2 


Input


5 4
1 2
2 3
3 4
4 5


Output


4 4 3 2 1 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
template <class t, class u>
void chmax(t& first, u second) {
  if (first < second) first = second;
}
template <class t, class u>
void chmin(t& first, u second) {
  if (second < first) first = second;
}
template <class t>
using vc = vector<t>;
template <class t>
using vvc = vc<vc<t>>;
using pi = pair<ll, ll>;
using vi = vc<ll>;
template <class t, class u>
ostream& operator<<(ostream& os, const pair<t, u>& p) {
  return os << "{" << p.first << "," << p.second << "}";
}
template <class t>
ostream& operator<<(ostream& os, const vc<t>& v) {
  os << "{";
  for (auto e : v) os << e << ",";
  return os << "}";
}
using uint = unsigned;
using ull = unsigned long long;
template <class t, size_t n>
ostream& operator<<(ostream& os, const array<t, n>& first) {
  return os << vc<t>(first.begin(), first.end());
}
template <ll i, class T>
void print_tuple(ostream&, const T&) {}
template <ll i, class T, class H, class... Args>
void print_tuple(ostream& os, const T& t) {
  if (i) os << ",";
  os << get<i>(t);
  print_tuple<i + 1, T, Args...>(os, t);
}
template <class... Args>
ostream& operator<<(ostream& os, const tuple<Args...>& t) {
  os << "{";
  print_tuple<0, tuple<Args...>, Args...>(os, t);
  return os << "}";
}
void print(ll x, ll suc = 1) {
  cout << x;
  if (suc == 1) cout << "\n";
  if (suc == 2) cout << " ";
}
ll read() {
  ll i;
  cin >> i;
  return i;
}
vi readvi(ll n, ll off = 0) {
  vi v(n);
  for (ll i = ll(0); i < ll(n); i++) v[i] = read() + off;
  return v;
}
template <class T>
void print(const vector<T>& v, ll suc = 1) {
  for (ll i = ll(0); i < ll(v.size()); i++)
    print(v[i], i == ll(v.size()) - 1 ? suc : 2);
}
string readString() {
  string s;
  cin >> s;
  return s;
}
template <class T>
T sq(const T& t) {
  return t * t;
}
void yes(bool ex = true) {
  cout << "Yes" << endl;
  if (ex) exit(0);
}
void no(bool ex = true) {
  cout << "No" << endl;
  if (ex) exit(0);
}
void possible(bool ex = true) {
  cout << "Possible" << endl;
  if (ex) exit(0);
}
void impossible(bool ex = true) {
  cout << "Impossible" << endl;
  if (ex) exit(0);
}
constexpr ll ten(ll n) { return n == 0 ? 1 : ten(n - 1) * 10; }
const ll infLL = LLONG_MAX / 3;
const ll inf = infLL;
ll topbit(signed t) { return t == 0 ? -1 : 31 - __builtin_clz(t); }
ll topbit(ll t) { return t == 0 ? -1 : 63 - __builtin_clzll(t); }
ll botbit(signed first) { return first == 0 ? 32 : __builtin_ctz(first); }
ll botbit(ll first) { return first == 0 ? 64 : __builtin_ctzll(first); }
ll popcount(signed t) { return __builtin_popcount(t); }
ll popcount(ll t) { return __builtin_popcountll(t); }
bool ispow2(ll i) { return i && (i & -i) == i; }
ll mask(ll i) { return (ll(1) << i) - 1; }
bool inc(ll first, ll second, ll c) { return first <= second && second <= c; }
template <class t>
void mkuni(vc<t>& v) {
  sort(v.begin(), v.end());
  v.erase(unique(v.begin(), v.end()), v.end());
}
ll rand_int(ll l, ll r) {
  static random_device rd;
  static mt19937_64 gen(rd());
  return uniform_int_distribution<ll>(l, r)(gen);
}
template <class t>
ll lwb(const vc<t>& v, const t& first) {
  return lower_bound(v.begin(), v.end(), first) - v.begin();
}
template <class E>
struct cactus {
  const vvc<E>& g;
  const ll n;
  vvc<ll> cs;
  vi vis, par, u;
  void dfs(ll v, ll p) {
    assert(vis[v] == 0);
    vis[v] = 1;
    par[v] = p;
    for (ll to : g[v])
      if (to != p) {
        if (vis[to] == 0)
          dfs(to, v);
        else if (vis[to] == 1) {
          ll x = v;
          vi z{x};
          while (x != to) {
            x = par[x];
            z.push_back(x);
          }
          cs.push_back(z);
        }
      }
    vis[v] = 2;
  }
  cactus(const vvc<E>& gg) : g(gg), n(g.size()), vis(n), par(n), u(n) {
    for (ll i = ll(0); i < ll(n); i++)
      if (!vis[i]) dfs(i, -1);
  }
};
signed main() {
  cin.tie(0);
  ios::sync_with_stdio(0);
  cout << fixed << setprecision(20);
  ll n, m;
  cin >> n >> m;
  vc<map<ll, ll>> id(n);
  vvc<ll> g(n);
  vc<pi> es;
  for (ll i = ll(0); i < ll(m); i++) {
    ll first, second;
    cin >> first >> second;
    first--;
    second--;
    id[first][second] = id[second][first] = i;
    g[first].push_back(second);
    g[second].push_back(first);
    es.emplace_back(first, second);
  }
  auto cs = cactus<ll>(g).cs;
  void(0);
  vi src(m, -1), val(m);
  for (auto c : cs)
    if (c.size() > 2) {
      ll s = c.size();
      vi d(s);
      for (ll i = ll(0); i < ll(s); i++) d[i] = id[c[i]][c[(i + 1) % s]];
      ll p = min_element(d.begin(), d.end()) - d.begin();
      ll q = max_element(d.begin(), d.end()) - d.begin();
      bool ok = true;
      for (ll i = p; i != q;) {
        ll j = (i + 1) % s;
        if (d[i] > d[j]) ok = false;
        i = j;
      }
      for (ll i = q; i != p;) {
        ll j = (i + 1) % s;
        if (d[i] < d[j]) ok = false;
        i = j;
      }
      if (ok) {
        src[d[p]] = d[q];
      }
    }
  vi cnt(n, 1);
  for (ll i = ll(m) - 1; i >= ll(0); i--) {
    ll first, second;
    tie(first, second) = es[i];
    cnt[first] = cnt[second] = val[i] = cnt[first] + cnt[second];
    if (src[i] != -1) {
      cnt[first] -= val[src[i]];
      cnt[second] -= val[src[i]];
    }
  }
  for (ll i = ll(0); i < ll(n); i++) cnt[i]--;
  print(cnt);
}

```