#include <bits/stdc++.h>
using namespace std;
set<pair<int, int> > forbid;
set<int> remaining;
int n, m, l, deg, x, y, comp, k;
bool ok(int a, int b) {
  if (a > b) swap(a, b);
  return (forbid.find({a, b}) == forbid.end());
}
void dfs(int nod) {
  vector<int> v;
  for (auto i : remaining)
    if (ok(nod, i)) v.push_back(i);
  for (auto i : v) remaining.erase(i);
  for (auto i : v) dfs(i);
}
int main() {
  cin >> n >> m >> k;
  for (int i = 2; i <= n; ++i) remaining.insert(i);
  deg = n - 1;
  for (int i = 0; i < m; ++i) {
    cin >> x >> y;
    if (x > y) swap(x, y);
    if (x == 1) --deg;
    forbid.insert({x, y});
  }
  if (deg < k) {
    cout << "impossible";
    return 0;
  }
  for (int i = 2; i <= n; ++i) {
    if (ok(1, i) && remaining.find(i) != remaining.end()) {
      ++comp;
      dfs(i);
    }
  }
  if (!remaining.empty() || comp > k) {
    cout << "impossible";
    return 0;
  }
  cout << "possible";
  return 0;
}
