#include <bits/stdc++.h>
using namespace std;
const long long M = 1e9 + 7;
long long expo(long long a, long long b) {
  if (b == 0) return 1;
  if (b % 2 == 0) {
    long long ret = expo(a, b / 2);
    ret = (ret * ret) % 1000000007;
    return ret;
  } else {
    long long ret = expo(a, b / 2);
    ret = (ret * ret) % 1000000007;
    ret = (ret * a) % 1000000007;
    return ret;
  }
}
bool is_prime(long long x) {
  if (x == 1) return false;
  for (long long i = 2; i * i <= x; i++)
    if (x % i == 0) return false;
  return true;
}
int arr[200005], sze[200005];
int root(int i) {
  while (arr[i] != i) i = arr[arr[i]];
  return i;
}
void unionn(int u, int v) {
  int a = root(u);
  int b = root(v);
  if (a == b) return;
  if (sze[a] > sze[b]) swap(a, b);
  arr[a] = arr[b];
  sze[b] += sze[a];
}
long long inf = 1e18;
vector<pair<int, int> > edges;
vector<int> v[200005], ans[200005];
set<int> st;
int vis[200005];
void solve(int x) {
  vis[x] = 1;
  for (int i = 0; i < v[x].size(); i++) {
    if (vis[v[x][i]] == 0 && v[x][i] != 1 && st.find(v[x][i]) == st.end()) {
      unionn(x, v[x][i]);
      ans[x].push_back(v[x][i]);
      solve(v[x][i]);
    }
  }
}
int main() {
  int n, m, d, x, y;
  cin >> n >> m >> d;
  for (int i = 1; i <= n; i++) {
    arr[i] = i;
    sze[i] = 1;
  }
  while (m--) {
    cin >> x >> y;
    if (x > y) swap(x, y);
    edges.push_back({x, y});
    v[x].push_back(y);
    v[y].push_back(x);
  }
  vector<int> t;
  for (int i = 0; i < edges.size(); i++) {
    if (edges[i].first == 1) {
      t.push_back(edges[i].second);
      st.insert(edges[i].second);
    }
  }
  if (t.size() < d) {
    cout << "NO" << endl;
  } else {
    sort(t.begin(), t.end());
    for (int i = 0; i < t.size(); i++) {
      solve(t[i]);
    }
    int x = t.size();
    for (int i = 0; i < t.size(); i++) {
      if (x == d) break;
      for (int j = 0; j < v[t[i]].size(); j++) {
        if (v[t[i]][j] != 1 && root(t[i]) != root(v[t[i]][j])) {
          ans[t[i]].push_back(v[t[i]][j]);
          unionn(t[i], v[t[i]][j]);
          x--;
          st.erase(t[i]);
          break;
        }
      }
    }
    bool h = true;
    for (int i = 0; i < t.size(); i++) {
      if (x == d) break;
      for (int j = 0; j < v[t[i]].size(); j++) {
        if (st.find(v[t[i]][j]) != st.end() && root(t[i]) != root(v[t[i]][j])) {
          x--;
          st.erase(v[t[i]][j]);
          ans[t[i]].push_back(v[t[i]][j]);
          unionn(t[i], v[t[i]][j]);
        }
        if (x == d) break;
      }
    }
    for (int i = t.size() - 1; i >= 0; i--) {
      if (x == d) break;
      if (st.find(t[i]) != st.end()) {
        for (int j = 0; j < v[t[i]].size(); j++) {
          if (v[t[i]][j] != 1 && root(t[i]) != root(v[t[i]][j])) {
            ans[v[t[i]][j]].push_back(t[i]);
            x--;
            st.erase(t[i]);
            break;
          }
        }
      }
      if (x == d) break;
    }
    if (x != d) {
      cout << "NO" << endl;
    } else {
      cout << "YES" << endl;
      set<int>::iterator it = st.begin();
      for (; it != st.end(); it++) {
        ans[1].push_back(*it);
      }
      for (int i = 1; i <= n; i++) {
        for (int j = 0; j < ans[i].size(); j++) {
          cout << i << ' ' << ans[i][j] << endl;
        }
      }
    }
  }
}
