#include <bits/stdc++.h>
using namespace std;
set<pair<long long, long long> > ex;
set<long long> rem;
bool allowed(long long a, long long b) {
  if (a > b) swap(a, b);
  return (ex.find({a, b}) == ex.end());
}
void dfs(long long src) {
  auto it = rem.upper_bound(1);
  while (it != rem.end()) {
    long long x = *it;
    if (allowed(src, x)) {
      rem.erase(it);
      dfs(x);
    }
    it = rem.upper_bound(x);
  }
}
signed main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  long long n, m, k;
  cin >> n >> m >> k;
  long long count = n - 1;
  for (long long i = 0; i < m; i++) {
    long long a, b;
    cin >> a >> b;
    if (a > b) swap(a, b);
    ex.insert({a, b});
    if (a == 1) count--;
  }
  if (count < k) {
    cout << "impossible";
    return 0;
  }
  for (long long i = 2; i <= n; i++) rem.insert(i);
  long long components = 0;
  for (long long i = 2; i <= n; i++) {
    if (allowed(1, i) && rem.find(i) != rem.end()) {
      dfs(i);
      components++;
    }
  }
  if (!rem.empty() || components > k) {
    cout << "impossible";
    return 0;
  }
  cout << "possible";
}
