1133F2.cpp

#include <bits/stdc++.h>
using namespace std;

#define int long long

#define ii pair<int,int>
#define fi first
#define sc second

#define sqr(x) ((x)*(x))
#define all(x) (x).begin(),(x).end()

#define rank qwertyui

const int N = 200005;

int root[N], rank[N];

int find(int i) {
  if (i == root[i]) return i;
  return root[i] = find(root[i]);
}

int join(int u, int v) {
  u = find(u); v = find(v);
  if (u == v) return false;
  if (rank[u] > rank[v]) swap(u, v);
  if (rank[u] == rank[v]) rank[v]++;
  root[u] = v;
  return true;
}

signed main() {
#ifdef _DEBUG
  freopen("in" , "r", stdin );
#endif
  ios::sync_with_stdio(0); cin.tie(0);
  int n, m, d;
  cin >> n >> m >> d;
  for (int i = 1; i <= n; i++) {
    root[i] = i;
  }
  set<int> s;
  vector<ii> e;
  for (int i = 1; i <= m; i++) {
    int u, v;
    cin >> u >> v;
    if (u > v) swap(u, v);
    if (u == 1) {
      s.insert(v);
      rank[v] = n;
    }
    else e.push_back(ii(u, v));
  }
  if (s.size() < d) {
    cout << "NO" << '\n';
    return 0;
  }
  vector<ii> r;
  for (auto i : e) {
    int u = find(i.fi), v = find(i.sc);
    if (!(s.count(u) && s.count(v))) {
      if (join(u, v)) r.push_back(ii(i.fi, i.sc));
    }
  }
  int t = s.size() - d;
  for (auto i : e) {
    if (!t) break;
    if (join(i.fi, i.sc)) {
      r.push_back(ii(i.fi, i.sc));
      t--;
    }
  }
  if (t) {
    cout << "NO" << '\n';
    return 0;
  }
  for (auto i : s) {
    if (join(1, i)) r.push_back(ii(1, i));
  }
  cout << "YES" << '\n';
  for (auto i : r) {
    cout << i.fi << ' ' << i.sc << '\n';
  }
}