#include <bits/stdc++.h>
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
using namespace std;
constexpr long long mod = 998244353;
const long long INF = mod * mod;
const double eps = 1e-6;
const double pi = acosl(-1.0);
long long mod_pow(long long x, long long n, long long m = mod) {
  if (n < 0) {
    long long res = mod_pow(x, -n, m);
    return mod_pow(res, m - 2, m);
  }
  if (abs(x) >= m) x %= m;
  if (x < 0) x += m;
  long long res = 1;
  while (n) {
    if (n & 1) res = res * x % m;
    x = x * x % m;
    n >>= 1;
  }
  return res;
}
struct modint {
  long long n;
  modint() : n(0) { ; }
  modint(long long m) : n(m) {
    if (n >= mod)
      n %= mod;
    else if (n < 0)
      n = (n % mod + mod) % mod;
  }
  operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) {
  a.n += b.n;
  if (a.n >= mod) a.n -= mod;
  return a;
}
modint operator-=(modint& a, modint b) {
  a.n -= b.n;
  if (a.n < 0) a.n += mod;
  return a;
}
modint operator*=(modint& a, modint b) {
  a.n = ((long long)a.n * b.n) % mod;
  return a;
}
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, long long n) {
  if (n == 0) return modint(1);
  modint res = (a * a) ^ (n / 2);
  if (n % 2) res = res * a;
  return res;
}
long long inv(long long a, long long p) {
  return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) {
  a = a / b;
  return a;
}
const int max_n = 1 << 21;
modint fact[max_n], factinv[max_n];
void init_f() {
  fact[0] = modint(1);
  for (int i = 0; i < max_n - 1; i++) {
    fact[i + 1] = fact[i] * modint(i + 1);
  }
  factinv[max_n - 1] = modint(1) / fact[max_n - 1];
  for (int i = max_n - 2; i >= 0; i--) {
    factinv[i] = factinv[i + 1] * modint(i + 1);
  }
}
modint comb(int a, int b) {
  if (a < 0 || b < 0 || a < b) return 0;
  return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
  if (a < 0 || b < 0 || a < b) return 0;
  return fact[a] * factinv[a - b];
}
string ok = "possible";
string ng = "impossible";
void solve() {
  int n, m, k;
  cin >> n >> m >> k;
  vector<vector<int>> G(n);
  for (int i = 0; i < m; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    G[a].push_back(b);
    G[b].push_back(a);
  }
  queue<int> q;
  set<int> s;
  for (int i = 1; i <= n - 1; i++) {
    s.insert(i);
  }
  int tmp = 0;
  vector<int> trans(n);
  while (s.size()) {
    vector<int> ids;
    q.push(*s.begin());
    s.erase(s.begin());
    while (!q.empty()) {
      int v = q.front();
      q.pop();
      ids.push_back(v);
      set<int> l;
      for (int to : G[v]) {
        if (s.count(to)) {
          s.erase(to);
          l.insert(to);
        }
      }
      for (int id : s) {
        q.push(id);
      }
      swap(s, l);
    }
    for (int id : ids) trans[id] = tmp;
    tmp++;
  }
  int le = 0, ri = 0;
  vector<int> tos;
  vector<bool> ban(n);
  for (int to : G[0]) ban[to] = true;
  for (int i = 1; i <= n - 1; i++) {
    if (ban[i]) continue;
    tos.push_back(trans[i]);
  }
  ri = tos.size();
  sort((tos).begin(), (tos).end());
  tos.erase(unique((tos).begin(), (tos).end()), tos.end());
  if (tos.size() != tmp) {
    cout << ng << "\n";
    return;
  }
  le = tos.size();
  if (le <= k && k <= ri) {
    cout << ok << "\n";
  } else {
    cout << ng << "\n";
  }
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(10);
  solve();
  return 0;
}
