// what is matter? never mind. 
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
//#pragma GCC target("sse,sse2,sse3,sse4,popcnt,abm,mmx,avx,avx2") 
#include<bits/stdc++.h>
#define For(i,a,b) for(int i=(a);i<=(b);++i)
#define Rep(i,a,b) for(int i=(a);i>=(b);--i)
#define ll long long
//#define int unsigned long long
#define ull unsigned long long
#define SZ(x) ((int)((x).size()))
#define ALL(x) (x).begin(),(x).end()
using namespace std;
inline int read()
{
    char c=getchar();int x=0;bool f=0;
    for(;!isdigit(c);c=getchar())f^=!(c^45);
    for(;isdigit(c);c=getchar())x=(x<<1)+(x<<3)+(c^48);
    if(f)x=-x;return x;
}

#define mod 1000000007
struct modint{
	int x;
	modint(int o=0){x=o;}
	modint &operator = (int o){return x=o,*this;}
	modint &operator +=(modint o){return x=x+o.x>=mod?x+o.x-mod:x+o.x,*this;}
	modint &operator -=(modint o){return x=x-o.x<0?x-o.x+mod:x-o.x,*this;}
	modint &operator *=(modint o){return x=1ll*x*o.x%mod,*this;}
	modint &operator ^=(int b){
		modint a=*this,c=1;
		for(;b;b>>=1,a*=a)if(b&1)c*=a;
		return x=c.x,*this;
	}
	modint &operator /=(modint o){return *this *=o^=mod-2;}
	friend modint operator +(modint a,modint b){return a+=b;}
	friend modint operator -(modint a,modint b){return a-=b;}
	friend modint operator *(modint a,modint b){return a*=b;}
	friend modint operator /(modint a,modint b){return a/=b;}
	friend modint operator ^(modint a,int b){return a^=b;}
	friend bool operator ==(modint a,modint b){return a.x==b.x;}
	friend bool operator !=(modint a,modint b){return a.x!=b.x;}
	bool operator ! () {return !x;}
	modint operator - () {return x?mod-x:0;}
	bool operator <(const modint&b)const{return x<b.x;}
};
inline modint qpow(modint x,int y){return x^y;}

vector<modint> fac,ifac,iv;
inline void initC(int n)
{
	if(iv.empty())fac=ifac=iv=vector<modint>(2,1);
	int m=iv.size(); ++n;
	if(m>=n)return;
	iv.resize(n),fac.resize(n),ifac.resize(n);
	For(i,m,n-1){
		iv[i]=iv[mod%i]*(mod-mod/i);
		fac[i]=fac[i-1]*i,ifac[i]=ifac[i-1]*iv[i];
	}
}
inline modint C(int n,int m){
	if(m<0||n<m)return 0;
	return initC(n),fac[n]*ifac[m]*ifac[n-m];
}
inline modint sign(int n){return (n&1)?(mod-1):(1);}

#define fi first
#define se second
#define pb push_back
#define mkp make_pair
typedef pair<int,int>pii;
typedef vector<int>vi;
 
#define maxn 200005
#define inf 0x3f3f3f3f

int n,m,k;
int e[17],es[1<<16];
modint f[1<<16]; // topo orders
modint g[17][1<<16],h[17][1<<16];

bool no(int s,int t){
	// no s->t
	return (es[s]&t)==0;
}

modint Cdown(int n,int m){
	return fac[n]*ifac[n-m];
}

void work()
{
	n=read(),m=read(),k=read();
	For(i,1,m){
		int u=read(),v=read();
		--u,--v;
		e[u]|=(1<<v);
	}
	For(i,1,(1<<n)-1){
		int t=__lg(i&-i);
		es[i]=es[i^(1<<t)]|e[t];
	}
//	For(i,0,(1<<n)-1) cout<<es[i]<<" "; cout<<" es\n";
	f[0]=1;
	For(s,0,(1<<n)-1)
		For(i,0,n-1)
			if(!(s>>i&1) && no((1<<i),s)) f[s|(1<<i)]+=f[s];
//	For(s,0,(1<<n)-1) cout<<f[s].x<<" "; cout<<" f\n";
	g[0][0]=1;
	h[0][0]=1;
	For(s,1,(1<<n)-1){
		int u=__lg(s&-s);
		int c=__builtin_popcount(s);
		for(int t=s;t;t=(t-1)&s){
			if(t>>u&1){
				if(no(t,s^t) && no(s^t,t)){
					For(i,1,c) g[i][s]+=g[i-1][s^t]*f[t];
				}
			}
		}
		for(int t=s;t;t=(t-1)&s){
			if(no(s^t,t)){
				For(i,1,c)
					For(j,1,i){
						if(j&1) h[i][s]+=g[j][t]*h[i-j][s^t];
						else h[i][s]-=g[j][t]*h[i-j][s^t];
					}
			}
		}
	}
//	For(s,0,(1<<n)-1) For(i,0,n) if(g[i][s].x) cout<<"g "<<i<<" "<<s<<" "<<g[i][s].x<<"\n";
//	For(s,0,(1<<n)-1) For(i,0,n) if(h[i][s].x) cout<<"h "<<i<<" "<<s<<" "<<h[i][s].x<<"\n";
	initC(n+k+50);
	modint res=0;
	For(i,1,n){
//		cout<<"hi "<<i<<" "<<h[i][(1<<n)-1].x<<"\n";
		modint coe=0;
		For(j,0,i-1)coe+=C(i-1,j)*sign(j)*Cdown(i-j+k,k);
		res+=coe*fac[i]*h[i][(1<<n)-1];
	}
	res*=ifac[n+k];
	cout<<res.x<<"\n";
}

signed main()
{
	int T=1;
	while(T--)work();
	return 0;
}
/*

*/