Submission #1048277

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Source Code Expand

#define DEB
#include<bits/stdc++.h>
#define REP(i,m) for(int i=0;i<(m);++i)
#define REPN(i,m,in) for(int i=(in);i<(m);++i)
#define ALL(t) (t).begin(),(t).end()
#define CLR(a) memset((a),0,sizeof(a))
#define pb push_back
#define mp make_pair
#define fr first
#define sc second

using namespace std;


#ifdef DEB
#define dump(x)  cerr << #x << " = " << (x) << endl
#define prl cerr<<"called:"<< __LINE__<<endl
#define dumpR(x) cerr<<"\x1b[31m"<<#x<<" = " <<(x)<<"\x1b[39m"<<endl
#define dumpY(x) cerr<<"\x1b[33m"<<#x<<" = " <<(x)<<"\x1b[39m"<<endl
#define dumpG(x) cerr<<"\x1b[32m"<<#x<<" = " <<(x)<<"\x1b[39m"<<endl
template<class T> void debug(T a,T b){ for(;a!=b;++a) cerr<<*a<<' ';cerr<<endl;}
#else
#define dump(x) ;
#define dumpR(x) ;
#define dumpY(x) ;
#define dumpG(x) ;
#define prl ;
template<class T> void debug(T a,T b){ ;}
#endif

template<class T> void chmin(T& a,const T& b) { if(a>b) a=b; }
template<class T> void chmax(T& a,const T& b) { if(a<b) a=b; }

typedef long long int lint;
typedef pair<int,int> pi;

namespace std{
  template<class S,class T>
  ostream &operator <<(ostream& out,const pair<S,T>& a){
    out<<'('<<a.fr<<','<<a.sc<<')';
    return out;
  }
}

//const int INF=5e8;
int n,m;
pi es[105];
int K;
bool valid[105];
template<lint mod>
struct Int_{
  unsigned x;
  unsigned mpow(Int_ a,unsigned k){
    Int_ res=1;
    while(k){
      if(k&1) res=res*a;
      a=a*a;
      k>>=1;
    }
    return res.x;
  }
  unsigned inverse(Int_ a){
    return mpow(a,mod-2);
  }
  Int_(): x(0) { }
  Int_(long long sig) {
    int sigt=sig%mod;
    if(sigt<0) sigt+=mod;
    x=sigt;
  }
  unsigned get() const { return (unsigned)x; }
  
  Int_ &operator+=(Int_ that) { if((x += that.x) >= mod) x -= mod; return *this; }
  Int_ &operator-=(Int_ that) { if((x += mod - that.x) >= mod) x -= mod; return *this; }
  Int_ &operator*=(Int_ that) { x = (unsigned long long)x * that.x % mod; return *this; }
  Int_ &operator=(Int_ that) { x=that.x; return *this;}
  Int_ &operator/=(Int_ that) { x=(unsigned long long) x * inverse(that.x)%mod; return *this;}
  bool operator==(Int_ that) const { return x==that.x; }
  bool operator!=(Int_ that) const { return x!=that.x; }

  Int_ operator-() const { return Int_(0)-Int_(*this);}
  Int_ operator+(Int_ that) const { return Int_(*this) += that; }
  Int_ operator-(Int_ that) const { return Int_(*this) -= that; }
  Int_ operator*(Int_ that) const { return Int_(*this) *= that; }
  Int_ operator/(Int_ that) const { return Int_(*this) /= that; }

};

namespace std{
  template<lint mod>
  ostream &operator <<(ostream& out,const Int_<mod>& a){
    out<<a.get();
    return out;
  }
  template<lint mod>
  istream &operator >>(istream& in,Int_<mod>& a){
    in>>a.x;
    return in;
  }
};

typedef Int_<1000000007> Int;
stack<pi> cur;
int low[200005],order[200005],cnt;

vector<int> g[55];
vector<pi>bicon;
int dfs(int v,int p){
  order[v]=cnt++;
  low[v]=order[v];
  for(auto e:g[v]){
    int to=e;
    if(order[to]<order[v]) cur.push(mp(v,to));
    if(order[to]==-1){
      low[v]=min(dfs(to,v),low[v]);
      if(low[to]>=order[v]){
        set<int> tmp;
        set<pi> es;
        while(1){
          pi t=cur.top();cur.pop();
          tmp.insert(t.fr);tmp.insert(t.sc);
          if(t.fr>t.sc){
            swap(t.fr,t.sc);
            es.insert(t);
            swap(t.fr,t.sc);
          }else{
            es.insert(t);
          }
          if(t.fr==v && t.sc==to) break;
        }
        bicon.pb(mp(tmp.size(),es.size()));
      }
    }else low[v]=min(low[v],order[to]);
  }
  return low[v];
}

Int mpow(Int a,int b){
  Int res=1;
  while(b){
    if(b&1) res=a*res;
    a=a*a;
    b>>=1;
  }
  return res;
}

Int solve(int a){
  Int res=0;
  REP(j,a) res+=mpow(K,__gcd(a,j));
  res/=a;
  return res;
}
Int C[205][205];
int deg[55];
int main(){
  REP(i,205){
    C[i][0]=1;
    REP(j,i) C[i][j+1]=C[i-1][j+1]+C[i-1][j];
  }

  cin>>n>>m>>K;
  REP(i,m){
    cin>>es[i].fr>>es[i].sc,--es[i].fr,--es[i].sc,valid[i]=1;
    ++deg[es[i].fr];
    ++deg[es[i].sc];
  }
  Int res=1;
  REP(i,n) if(deg[i]==1){
    REP(j,m) if(valid[j] && (es[j].fr==i || es[j].sc==i)){
      valid[j]=false;
      --deg[es[j].fr];
      --deg[es[j].sc];
      res*=K;
    }
  }
  REP(i,m) if(valid[i]){
    g[es[i].fr].pb(es[i].sc);
    g[es[i].sc].pb(es[i].fr);
  }
  memset(low,-1,sizeof(low));
  memset(order,-1,sizeof(order));
  REP(i,n) if(low[i]==-1) dfs(i,-1);

  for(auto S:bicon){
    if(S.fr==S.sc) res*=solve(S.fr);
    else res*=C[S.sc+K-1][K-1];
  }
  cout<<res<<endl;
  return 0;
}

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