#include<bits/stdc++.h>
using namespace std;
using Int = long long;
template<typename T1,typename T2> inline void chmin(T1 &a,T2 b){if(a>b) a=b;}
template<typename T1,typename T2> inline void chmax(T1 &a,T2 b){if(a<b) a=b;}


template<typename T,T MOD = 1000000007>
struct Mint{
  T v;
  Mint():v(0){}
  Mint(signed v):v(v){}
  Mint(long long t){v=t%MOD;if(v<0) v+=MOD;}

  Mint pow(long long k){
    Mint res(1),tmp(v);
    while(k){
      if(k&1) res*=tmp;
      tmp*=tmp;
      k>>=1;
    }
    return res;
  }
  
  static Mint add_identity(){return Mint(0);}
  static Mint mul_identity(){return Mint(1);}
  
  Mint inv(){return pow(MOD-2);}
  
  Mint& operator+=(Mint a){v+=a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator-=(Mint a){v+=MOD-a.v;if(v>=MOD)v-=MOD;return *this;}
  Mint& operator*=(Mint a){v=1LL*v*a.v%MOD;return *this;}
  Mint& operator/=(Mint a){return (*this)*=a.inv();}
  
  Mint operator+(Mint a) const{return Mint(v)+=a;};
  Mint operator-(Mint a) const{return Mint(v)-=a;};
  Mint operator*(Mint a) const{return Mint(v)*=a;};
  Mint operator/(Mint a) const{return Mint(v)/=a;};

  Mint operator-() const{return v?Mint(MOD-v):Mint(v);}

  bool operator==(const Mint a)const{return v==a.v;}
  bool operator!=(const Mint a)const{return v!=a.v;}
  bool operator <(const Mint a)const{return v <a.v;}

  // find x s.t. a^x = b
  static T log(T a,T b){
    const T sq=40000;
    unordered_map<T, T> dp;
    dp.reserve(sq);
    Mint res(1);
    for(Int r=0;r<sq;r++){
      if(!dp.count(res.v)) dp[res.v]=r;
      res*=a;
    }
    Mint p=Mint(a).inv().pow(sq);
    res=b;
    for(Int q=0;q<=MOD/sq+1;q++){
      if(dp.count(res.v)){
        T idx=q*sq+dp[res.v];
        if(idx>0) return idx;
      }
      res*=p;
    }
    assert(0);
    return T(-1);
  }
  
  static Mint comb(long long n,Int k){
    Mint num(1),dom(1);
    for(Int i=0;i<k;i++){
      num*=Mint(n-i);
      dom*=Mint(i+1);
    }
    return num/dom;
  }
};


template<typename M>
struct Enumeration{
  static vector<M> fact,finv,invs;
  
  static void init(Int n){
    Int m=fact.size();
    if(n<m) return;
    
    fact.resize(n+1,1);
    finv.resize(n+1,1);
    invs.resize(n+1,1);
    
    if(m==0) m=1;
    for(Int i=m;i<=n;i++) fact[i]=fact[i-1]*M(i);
    finv[n]=M(1)/fact[n];
    for(Int i=n;i>=m;i--) finv[i-1]=finv[i]*M(i);
    for(Int i=m;i<=n;i++) invs[i]=finv[i]*fact[i-1];
  }
  
  static M C(Int n,Int k){
    if(n<k||k<0) return M(0);
    init(n);
    return fact[n]*finv[n-k]*finv[k];
  }

  static M P(Int n,Int k){
    if(n<k||k<0) return M(0);
    init(n);
    return fact[n]*finv[n-k];
  }
  
  static M H(Int n,Int k){
    if(n<0||k<0) return M(0);
    if(!n&&!k) return M(1);
    init(n+k-1);
    return C(n+k-1,k);
  }

  static M S(Int n,Int k){
    M res;
    init(k);
    for(Int i=1;i<=k;i++){
      M tmp=C(k,i)*M(i).pow(n);
      if((k-i)&1) res-=tmp;
      else res+=tmp;
    }    
    return res*=finv[k];
  }

  static vector<vector<M> > D(Int n,Int m){
    vector<vector<M> > dp(n+1,vector<M>(m+1,0));
    dp[0][0]=M(1);
    for(Int i=0;i<=n;i++){
      for(Int j=1;j<=m;j++){
        if(i-j>=0) dp[i][j]=dp[i][j-1]+dp[i-j][j];
        else dp[i][j]=dp[i][j-1];
      }
    }
    return dp;
  }

  static M B(Int n,Int k){
    if(n==0) return M(1);
    k=min(k,n);
    init(k);    
    vector<M> dp(k+1);
    dp[0]=M(1);
    for(Int i=1;i<=k;i++)
      dp[i]=dp[i-1]+((i&1)?-finv[i]:finv[i]);    
    M res;
    for(Int i=1;i<=k;i++)
      res+=M(i).pow(n)*finv[i]*dp[k-i];    
    return res;
  }

  static M montmort(Int n){
    M res;
    init(n);
    for(Int k=2;k<=n;k++){
      if(k&1) res-=finv[k];
      else res+=finv[k];
    }
    return res*=fact[n];
  }

  static M LagrangePolynomial(vector<M> &y,M t){
    Int n=y.size()-1;    
    if(t.v<=n) return y[t.v];
    init(n+1);
    M num(1);
    for(Int i=0;i<=n;i++) num*=t-M(i);
    M res;
    for(Int i=0;i<=n;i++){
      M tmp=y[i]*num/(t-M(i))*finv[i]*finv[n-i];
      if((n-i)&1) res-=tmp;
      else res+=tmp;
    }
    return res;
  }
};
template<typename M>
vector<M> Enumeration<M>::fact = vector<M>();
template<typename M>
vector<M> Enumeration<M>::finv = vector<M>();
template<typename M>
vector<M> Enumeration<M>::invs = vector<M>();


struct UnionFind{
  Int n,num;
  vector<Int> r,p;
  UnionFind(){}
  UnionFind(Int sz):n(sz),num(sz),r(sz,1),p(sz,0){iota(p.begin(),p.end(),0);}
  Int find(Int x){
    return (x==p[x]?x:p[x]=find(p[x]));
  }
  bool same(Int x,Int y){
    return find(x)==find(y);
  }
  void unite(Int x,Int y){
    x=find(x);y=find(y);
    if(x==y) return;
    if(r[x]<r[y]) swap(x,y);
    r[x]+=r[y];
    p[y]=x;
    num--;
  }
  Int size(Int x){
    return r[find(x)];
  }
  Int count() const{
    return num;
  }
};

struct BiconnectedComponent {
  vector<Int> ord, low;
  vector<bool> used;
  vector<vector<Int>> g;
  vector<vector<pair<Int, Int>>> bc;
  vector<pair<Int, Int>> tmp;
  Int n, k = 0;
  BiconnectedComponent(const vector<vector<Int>> &g) : g(g) {
    n = g.size();
    ord.resize(n, -1);
    low.resize(n, -1);
    used.resize(n, false);
  }
  void dfs(Int u, Int prev) {
    used[u] = true;
    ord[u] = k ++;
    low[u] = ord[u];
    Int cnt = 0;
    for (auto v : g[u]) if (v != prev) {
        if (ord[v] < ord[u]) { 
          tmp.emplace_back(min(u, v), max(u, v));
        }
        if (!used[v]) {
          cnt ++;
          dfs(v, u);
          low[u] = min(low[u], low[v]);
          if (low[v] >= ord[u]) {
            bc.push_back({});
            while (true) {
              pair<Int, Int> e = tmp.back();
              bc.back().emplace_back(e);
              tmp.pop_back();
              if (min(u, v) == e.first && max(u, v) == e.second) {
                break;
              }
            }
          }
        } else {
          low[u] = min(low[u], ord[v]);
        }
      }
  }
};

//INSERT ABOVE HERE
signed main(){
  Int n,m,k;
  cin>>n>>m>>k;

  using P = pair<Int, Int>;
  map<P, Int> idx;
  vector<vector<Int>> G(n);
  for(Int i=0;i<m;i++){
    Int a,b;
    cin>>a>>b;
    a--;b--;
    G[a].emplace_back(b);
    G[b].emplace_back(a);
    idx[P(a,b)]=idx[P(b,a)]=i;
  }

  BiconnectedComponent bc(G);
  for(Int i=0;i<n;i++){
    if(bc.used[i]) continue;
    bc.dfs(i,-1);
  }
  
  UnionFind uf(m);
  for(auto vs:bc.bc)
    for(auto p:vs) uf.unite(idx[p],idx[vs[0]]);  

  vector<set<Int>> cnt(m);  
  for(auto vs:bc.bc){
    for(auto p:vs){
      cnt[uf.find(idx[p])].emplace(p.first);     
      cnt[uf.find(idx[p])].emplace(p.second);
    }
  }
  
  using M = Mint<Int>;
  using E = Enumeration<M>;
  E::init(1e5);

  vector<M> dp1(m+1),dp2(m+1);
  vector<Int> used1(m+1,0),used2(m+1,0);
  
  auto calc1=
    [&](Int x)->M{
      if(used1[x]) return dp1[x];
      used1[x]=1;      
      M &res=dp1[x];
      res=M(0);
      
      for(Int i=0;i<x;i++)
        res+=M(k).pow(__gcd(i,x));
      
      res*=E::invs[x];
      return res;
    };

  M ans{1};
  for(Int i=0;i<m;i++){
    if(uf.find(i)!=i) continue;
    if(uf.size(i)< (Int)cnt[i].size()) ans*=M(k).pow(uf.size(i));
    if(uf.size(i)==(Int)cnt[i].size()) ans*=calc1(uf.size(i));
    if(uf.size(i)> (Int)cnt[i].size()) ans*=E::H(k,uf.size(i));
  }  
  cout<<ans.v<<endl;
  return 0;
}


Measured memory_bytes: 2688