// ref. https://ei1333.github.io/luzhiled/snippets/graph/bi-connected-components.html
// ref. https://kmjp.hatenablog.jp/entry/2016/11/30/0930

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <unordered_map>
#include <vector>
#include <string.h>
#include <set>

using namespace std;

#define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl

template<class T> void printvec(const vector<T>& v) {
  for (auto x : v) { cout << x << " "; }
  cout << endl;
}
template<class T> void printtree(const vector< vector<T> >& tree) {
  for (long long i = 0; i < tree.size(); ++i) {
    cout << i + 1 << ": "; printvec(tree[i]);
  }
}
template<class T, class U> void printmap(const map<T, U>& mp) {
  for (auto x : mp) { cout << x.first << "=>" << x.second << endl; }
}

template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return true; } return false; }

#define rep(i, n) for(ll i = 0; i < n; ++i)
#define all(s) s.begin(), s.end()
#define sz(x) (ll)(x).size()
#define fr first
#define sc second
#define mp make_pair
#define pb push_back
#define eb emplace_back

typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll, ll> P;
typedef tuple<ll, ll, ll> triple;
typedef double D;
typedef vector<ll> vl;
typedef vector<P> vp;

const ll INF = 1e9;
const ll MOD = 1000000007;  // 1e9 + 7

// LowLink
template<typename G>
struct LowLink {
  const G &g;
  vector<int> used, ord, low;
  vector<int> articulation;
  vector<pair<int, int>> bridge;

  LowLink(const G &g) : g(g) {}

  int dfs(int idx, int k, int par) {
    used[idx] = true;
    ord[idx] = k++;
    low[idx] = ord[idx];
    bool is_articulation = false;
    int cnt = 0;
    for(auto &to : g[idx]) {
      if(!used[to]) {
        ++cnt;
        k = dfs(to, k, idx);
        low[idx] = min(low[idx], low[to]);
        is_articulation |= ~par && low[to] >= ord[idx];
        if(ord[idx] < low[to]) bridge.emplace_back(minmax(idx, (int) to));
      } else if(to != par) {
        low[idx] = min(low[idx], ord[to]);
      }
    }
    is_articulation |= par == -1 && cnt > 1;
    if(is_articulation) articulation.push_back(idx);
    return k;
  }

  virtual void build() {
    used.assign(g.size(), 0);
    ord.assign(g.size(), 0);
    low.assign(g.size(), 0);
    int k = 0;
    for(int i = 0; i < g.size(); i++) {
      if(!used[i]) k = dfs(i, k, -1);
    }
  }
};

// BiConnectedComponents
// cf. https://ei1333.github.io/luzhiled/snippets/graph/bi-connected-components.html
template<typename G>
struct BiConnectedComponents : LowLink<G> {
  using LL = LowLink< G >;

  vector<int> used;
  vector<vector<pair<int, int>>> bc;
  vector<pair<int, int>> tmp;

  BiConnectedComponents(const G &g) : LL(g) {}

  void dfs(int idx, int par) {
    used[idx] = true;
    for(auto &to : this->g[idx]) {
      if(to == par) continue;
      if(!used[to] || this->ord[to] < this->ord[idx]) {
        tmp.emplace_back(minmax(idx, to));
      }
      if(!used[to]) {
        dfs(to, idx);
        if(this->low[to] >= this->ord[idx]) {
          bc.emplace_back();
          for(;;) {
            auto e = tmp.back();
            bc.back().emplace_back(e);
            tmp.pop_back();
            if(e.first == min(idx, to) && e.second == max(idx, to)) {
              break;
            }
          }
        }
      }
    }
  }

  void build() override {
    LL::build();
    used.assign(this->g.size(), 0);
    for(int i = 0; i < used.size(); i++) {
      if(!used[i]) dfs(i, -1);
    }
  }
};

// Mod int
// cf. https://www.youtube.com/watch?v=1Z6ofKN03_Y
struct mint {
  ll x;
  mint(ll x = 0) : x((x + MOD) % MOD) {}
  mint& operator+= (const mint a) {
    if ((x += a.x) >= MOD) x %= MOD;
    return *this;
  }
  mint operator+ (const mint a) const {
    mint res(*this);
    return res += a;
  }
  mint& operator-= (const mint a) {
    if ((x += MOD - a.x) >= MOD) x %= MOD;
    return *this;
  }
  mint operator- (const mint a) const {
    mint res(*this);
    return res -= a;
  }
  mint& operator*= (const mint a) {
    (x *= a.x) %= MOD;
    return *this;
  }
  mint operator* (const mint a) const {
    mint res(*this);
    return res *= a;
  }
  mint pow(ll t) const {
    if (!t) { return 1; }
    mint a = pow(t >> 1);
    a *= a;
    if (t & 1) a *= *this;
    return a;
  }

  // for prime mod
  mint inv() const {
    return pow(MOD-2);
  }
  mint& operator/= (const mint a) {
    return (*this) *= a.inv();
  }
  mint operator/ (const mint a) const {
    mint res(*this);
    return res /= a;
  }
};
istream& operator>>(istream& is, const mint& a) { return is >> a.x;}
ostream& operator<<(ostream& os, const mint& a) { return os << a.x;}

// int main(int argc, char** argv) {
//   // int p;
//   // cin >> p;
//
//   MOD = 13;
//   mint p(10);
//   cout << (p + 15).x << endl;   // 12 (25 % 13)
//   cout << (p - 15).x << endl;   // 8  (-5 % 13)
//   cout << (p * 2).x << endl;    // 7  (20 % 13)
//   cout << (p.pow(3)).x << endl; // 12 (1000 % 13)
//   cout << (p / 3).x << endl;    // 12 (12 * 3 = 10 (36 % 13))
//
//   mint p2(-3);
//   cout << p2.x << endl; // 10 (-3 % 13)

// Combination mod prime.
// cf. https://www.youtube.com/watch?v=1Z6ofKN03_Y
struct Combination {
  vector<mint> fact, ifact;
  Combination(int n) { init(n); }
  void init(int n) {
    assert(n < MOD); // n must be lower than MOD.

    fact.resize(n + 1);
    ifact.resize(n + 1);

    fact[0] = 1;
    for (int i = 1; i <= n; ++i) { fact[i] = fact[i-1] * i; }
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i) { ifact[i-1] = ifact[i] * i; }
  }
  mint operator() (int n, int k) const {
    if (k < 0 || k > n) { return 0; }
    return fact[n] * ifact[k] * ifact[n-k];
  }
  mint perm(int n, int k) const {
    if (k < 0 || k > n) { return 0; }
    return fact[n] * ifact[n-k];
  }
};

// int main(int argc, char** argv) {
//   MOD = 13;
//
//   Combination c(12);
//   cout << c(12, 0).x << endl;  // 1  = 1 % 13
//   cout << c(12, 1).x << endl;  // 12 = 12 % 13
//   cout << c(12, 2).x << endl;  // 1  = 66 % 13 = (12 * 11 / 2) % 13
//   cout << c(12, 3).x << endl;  // 12 = 220 % 13 = (12 * 11 * 10 / (3 * 2 * 1)) % 13
//   cout << c(12, 11).x << endl; // 12 = 12 % 13
//   cout << c(12, 12).x << endl; // 1  = 12 % 13
//
//   cout << c.perm(12, 3).x << endl; // 7 = 12 * 11 * 10 % 13
// }

int64_t euler_phi(int64_t n) {
  int64_t ret = n;
  for(int64_t i = 2; i * i <= n; i++) {
    if(n % i == 0) {
      ret -= ret / i;
      while(n % i == 0) n /= i;
    }
  }
  if(n > 1) ret -= ret / n;
  return ret;
}

int main(int argc, char** argv) {
  cin.tie(NULL);
  cout.tie(NULL);
  ios_base::sync_with_stdio(false);
  //cout << setprecision(10) << fixed;

  ll n,m,k;
  cin >> n >> m >> k;
  vector<vector<int>> g(n);
  Combination comb(101010);

  rep(iter,m) {
    int a,b;
    cin >> a >> b;
    --a;--b;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  BiConnectedComponents<vector<vector<int>>> bcc(g);
  bcc.build();

  mint ans = 1;
  for (vector<pair<int, int>>& vs : bcc.bc) {
    set<int> vertex;
    for (auto& p : vs) {
      vertex.emplace(p.first);
      vertex.emplace(p.second);
    }
    if (vertex.size() == vs.size()) { // simple cycle
      mint now = 0;
      for (int i = 1; i <= vertex.size(); ++i) {
        if (vertex.size()%i == 0) {
          now += mint(k).pow(vertex.size()/i) * euler_phi(i);
        }
      }
      now /= vertex.size();
      ans *= now;
    } else { // paint k colors on vs.size() vertices.
      ans *= comb(k + vs.size() - 1, vs.size()); // kH(vs.size())
    }
  }

  cout << ans << endl;
}


Measured memory_bytes: 1792