#include <bits/stdc++.h>
using namespace std;
set<int> unseen;
set<int> uadj[300005];
int ci[300005], C;
int nin[300005];
int n, m, k;
void go(int i, int cn) {
  ci[i] = cn;
  unseen.erase(unseen.find(i));
  int j = 0;
  while (1) {
    auto it = unseen.lower_bound(j + 1);
    if (it == unseen.end()) break;
    j = *it;
    if (!uadj[i].count(j)) {
      go(j, cn);
    }
  }
}
int main() {
  scanf("%d %d %d", &n, &m, &k);
  for (int i = (0); i < (m); i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    uadj[x].insert(y);
    uadj[y].insert(x);
  }
  for (int i = (2); i < (n + 1); i++) unseen.insert(i);
  for (int i = (2); i < (n + 1); i++)
    if (ci[i] == 0) {
      go(i, ++C);
    }
  for (int i = (2); i < (n + 1); i++) {
    if (!uadj[1].count(i)) nin[ci[i]]++;
  }
  int tsum = 0;
  for (int i = (1); i < (C + 1); i++) {
    tsum += nin[i];
    if (nin[i] == 0) {
      printf("impossible\n");
      return 0;
    }
  }
  if (C <= k && k <= tsum) {
    printf("possible\n");
  } else {
    printf("impossible\n");
  }
}
