#include <bits/stdc++.h>
using namespace std;
set<int> remain;
set<pair<int, int> > forbid;
bool allowed(int a, int b) {
  if (a > b) swap(a, b);
  return forbid.find(make_pair(a, b)) == forbid.end();
}
void dfs(int x) {
  vector<int> neigh;
  for (int y : remain) {
    if (allowed(x, y)) neigh.push_back(y);
  }
  for (int n : neigh) {
    remain.erase(n);
  }
  for (int y : neigh) {
    dfs(y);
  }
}
int main() {
  int N, M, K;
  cin >> N >> M >> K;
  int e1 = N - 1;
  for (int i = 2; i <= N; i++) remain.insert(i);
  for (int i = 0; i < M; i++) {
    int a, b;
    cin >> a >> b;
    if (a > b) swap(a, b);
    forbid.insert(make_pair(a, b));
    if (a == 1) e1--;
  }
  if (e1 < K) {
    cout << "impossible" << endl;
    return 0;
  }
  int n1neigh = 0;
  for (int i = 2; i <= N; i++) {
    if (allowed(1, i) && (remain.find(i) != remain.end())) {
      dfs(i);
      n1neigh++;
    }
  }
  if (!remain.empty() || n1neigh > K) {
    cout << "impossible" << endl;
    return 0;
  }
  cout << "possible" << endl;
  return 0;
}
