#include <bits/stdc++.h>
using namespace std;
const string yes = "possible";
const string no = "impossible";
const int MX = 300005;
int n, m, k, p[MX];
set<int> st[MX], ex;
int parent(int a) { return a == p[a] ? a : p[a] = parent(p[a]); }
void join(int a, int b) { p[parent(a)] = parent(b); }
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> m >> k;
  for (int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    if (b > 1) st[a].insert(b);
    if (a > 1) st[b].insert(a);
  }
  iota(p, p + MX, 0);
  for (int i = 0; i < n; i++) ex.insert(i + 1);
  ex.erase(1);
  for (int i = 2; i <= n; i++)
    if (ex.count(i)) {
      queue<int> p;
      ex.erase(i);
      auto it = ex.begin();
      while (it != ex.end()) {
        int x = *it;
        if (!st[i].count(x)) {
          p.push(x);
          join(i, x);
          auto aux = it;
          it++;
          ex.erase(*aux);
        } else {
          it++;
        }
      }
      while (p.size()) {
        int j = p.front();
        p.pop();
        it = st[i].begin();
        for (int x : st[j]) {
          while (it != st[i].end() && *it < x) {
            if (ex.count(*it)) p.push(*it);
            join(i, *it);
            ex.erase(*it);
            auto aux = it;
            it++;
            st[i].erase(aux);
          }
          if (it != st[i].end() && *it == x) it++;
        }
        while (it != st[i].end()) {
          if (ex.count(*it)) p.push(*it);
          join(i, *it);
          ex.erase(*it);
          auto aux = it;
          it++;
          st[i].erase(*aux);
        }
      }
    }
  int ned = 0, op = 0;
  for (int i = 2; i <= n; i++)
    if (!st[1].count(i))
      if (parent(1) != parent(i)) {
        join(1, i);
        ned++;
      } else {
        op++;
      }
  if (ned <= k && k <= ned + op) {
    for (int i = 2; i <= n; i++)
      if (parent(1) != parent(i)) {
        cout << no << '\n';
        return 0;
      }
    cout << yes << '\n';
  } else {
    cout << no << '\n';
  }
  return 0;
}
