#include <bits/stdc++.h>
using namespace std;
int lr[300005], boo[300005], bo, n, m, k;
set<int> cant[300005];
set<int> a;
void bfs(int x) {
  int l = 1, r = 1;
  lr[1] = x;
  boo[x] = 1;
  vector<int> tt;
  tt.clear();
  do {
    for (auto i : a) {
      if (i != lr[l] && cant[lr[l]].count(i) == 0 && boo[i] == 0) {
        boo[i] = 1;
        lr[++r] = i;
        tt.push_back(i);
      }
    }
    if (cant[lr[l]].count(1) == 0) bo = 1;
    for (auto i : tt) a.erase(i);
    tt.clear();
    ++l;
  } while (l <= r);
}
int main() {
  scanf("%d%d%d", &n, &m, &k);
  for (int i = 2; i <= n; i++) a.insert(i);
  for (int i = 1; i <= m; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    if (x > y) swap(x, y);
    if (x == 1) ++bo;
    cant[x].insert(y);
    cant[y].insert(x);
  }
  if (n - bo - 1 < k) {
    puts("impossible");
    return 0;
  }
  for (int i = 2; i <= n; i++)
    if (!boo[i] && a.count(i)) {
      bo = 0;
      bfs(i);
      if (!bo) {
        puts("impossible");
        return 0;
      }
    }
  if (((a.size()) > k)) printf("im");
  puts("possible");
}
