#include <bits/stdc++.h>
using namespace std;
set<int> v[500001];
set<int> st;
set<int>::iterator it;
void dfs(int i) {
  vector<int> v3;
  for (it = st.begin(); it != st.end(); ++it) {
    if (v[i].find(*it) == v[i].end()) {
      v3.push_back(*it);
    }
  }
  for (int j = 0; j < v3.size(); ++j) {
    st.erase(st.find(v3[j]));
  }
  for (int j = 0; j < v3.size(); ++j) dfs(v3[j]);
}
int main() {
  std::ios::sync_with_stdio(false);
  int T;
  T = 1;
  while (T--) {
    int n, m, i, j, a, b, ct = 0, k;
    cin >> n >> m >> k;
    for (i = 2; i <= n; ++i) st.insert(i);
    for (i = 0; i < m; ++i) {
      cin >> a >> b;
      v[a].insert(b);
      v[b].insert(a);
    }
    if (n - 1 - v[1].size() < k) {
      cout << "impossible" << endl;
      return 0;
    }
    for (i = 2; i <= n; ++i) {
      if (v[1].find(i) == v[1].end() && st.find(i) != st.end()) {
        ++ct;
        dfs(i);
      }
    }
    if (ct > k || st.size() > 0) {
      cout << "impossible" << endl;
      return 0;
    }
    cout << "possible" << endl;
  }
  return 0;
}
