#include <bits/stdc++.h>
using namespace std;
std::map<pair<int, int>, bool> m;
set<int> s;
set<pair<int, int> > s1;
bool isfind(int a, int b) {
  if (a > b) swap(a, b);
  return s1.find(make_pair(a, b)) == s1.end();
}
void dfs(int x) {
  std::vector<int> v;
  for (int i : s) {
    if (isfind(x, i)) v.push_back(i);
  }
  for (int i = 0; i < v.size(); i++) {
    s.erase(v[i]);
  }
  for (int i = 0; i < v.size(); i++) {
    dfs(v[i]);
  }
}
int main(int argc, char const *argv[]) {
  int n, m, k;
  cin >> n >> m >> k;
  int x, y;
  int cnt = n - 1;
  for (int i = 2; i <= n; ++i) {
    s.insert(i);
  }
  for (int i = 0; i < m; ++i) {
    cin >> x >> y;
    if (x > y) swap(x, y);
    s1.insert(make_pair(x, y));
    if (x == 1) cnt--;
  }
  if (cnt < k) {
    cout << "impossible";
    return 0;
  }
  int comp = 0;
  for (int i = 2; i <= n; ++i) {
    if (isfind(1, i) && s.find(i) != s.end()) {
      dfs(i);
      comp++;
    }
  }
  if (comp > k) {
    cout << "impossible";
    return 0;
  }
  if (!s.empty()) {
    cout << "impossible";
    return 0;
  }
  cout << "possible";
  return 0;
}
