#include<cstdio>
#include<vector>
#include<queue>
#include<cstring>
#include<iostream>
#include<algorithm>
#include<set>
#include<map>
#include<ctime>
#include<random>
#include<array>
#include<assert.h>
// #define int long long
#define pb emplace_back
#define mp make_pair
#define fi first
#define se second
#define dbg(x) cerr<<"In Line "<< __LINE__<<" the "<<#x<<" = "<<x<<'\n'
#define dpi(x,y) cerr<<"In Line "<<__LINE__<<" the "<<#x<<" = "<<x<<" ; "<<"the "<<#y<<" = "<<y<<'\n'
#define DE(fmt,...) fprintf(stderr, "Line %d : " fmt "\n",__LINE__,##__VA_ARGS__)
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int>pii;
typedef pair<ll,int>pli;
typedef pair<ll,ll>pll;
typedef pair<int,ll>pil;
typedef vector<int>vi;
typedef vector<ll>vll;
typedef vector<pii>vpii;
typedef vector<pll>vpll;
template<typename T>T cmax(T &x, T y){return x=x>y?x:y;}
template<typename T>T cmin(T &x, T y){return x=x<y?x:y;}
template<typename T>
T &read(T &r){
	r=0;bool w=0;char ch=getchar();
	while(ch<'0'||ch>'9')w=ch=='-'?1:0,ch=getchar();
	while(ch>='0'&&ch<='9')r=r*10+(ch^48),ch=getchar();
	return r=w?-r:r;
}
template<typename T1,typename... T2>
void read(T1 &x,T2& ...y){read(x);read(y...);}
const int mod=1000000007;
inline void cadd(int &x,int y){x=(x+y>=mod)?(x+y-mod):(x+y);}
inline void cdel(int &x,int y){x=(x-y<0)?(x-y+mod):(x-y);}
inline int add(int x,int y){return (x+y>=mod)?(x+y-mod):(x+y);}
inline int del(int x,int y){return (x-y<0)?(x-y+mod):(x-y);}
int qpow(int x,int y){
	int s=1;
	while(y){
		if(y&1)s=1ll*s*x%mod;
		x=1ll*x*x%mod;
		y>>=1;
	}
	return s;
}
const int N=17;
const int M=(1<<16)+10;
inline int bit(int x){return 1<<x;}
inline int subin(int x,int S){return ((1<<(x-1))&S)>0;}
int n,m,k;
int fac[110],inv[110];
int C(int x,int y){return 1ll*fac[x]*inv[y]%mod*inv[x-y]%mod;}
int e[N][N];
int kcf[N];
int dp[N][N];
int f[M],fdp[M],fr[N],nx[N];
int g[N][M],h[N][M];
int frs[M];
int ans=0;
signed main(){
	// #ifdef do_while_true
		// assert(freopen("timeline.in","r",stdin));
		// assert(freopen("timline.out","w",stdout));
	// #endif
	n=100;
	fac[0]=1;for(int i=1;i<=n;i++)fac[i]=1ll*fac[i-1]*i%mod;
	inv[n]=qpow(fac[n],mod-2);for(int i=n-1;~i;--i)inv[i]=1ll*inv[i+1]*(i+1)%mod;
	read(n,m,k);
	for(int len=1;len<=n;len++){
		memset(dp,0,sizeof(dp));
		dp[1][0]=1;
		for(int i=1;i<=len;i++){
			for(int j=0;j<=k;j++){
				cadd(dp[i+1][j+1],1ll*dp[i][j]*(len-i)%mod);
				if(j<n)
					cadd(dp[i][j+1],1ll*dp[i][j]*(i+j+1)%mod);
			}
		}
		kcf[len]=dp[len][k];
		dpi(len,kcf[len]);
	}
	for(int i=1,u,v;i<=m;i++){
		read(u,v);
		e[u][v]=1;
	}
	for(int k=1;k<=n;k++)
		for(int i=1;i<=n;i++)
			for(int j=1;j<=n;j++)
				if(e[i][k]&&e[k][j])
					e[i][j]=1;
	for(int i=1;i<=n;i++)
		for(int j=1;j<=n;j++)
			if(e[i][j])
				fr[j]|=bit(i-1),nx[i]|=bit(j-1);
	for(int i=1;i<bit(n);i++){
		frs[i]=frs[i-(i&(-i))]|fr[__lg(i&(-i))+1];
	}
	f[0]=1;
	for(int S=1;S<bit(n);S++){
		int fl=1;
		for(int i=1;i<=n;i++)if(!subin(i,S)){
			int ok0=0,ok1=0;
			for(int j=1;j<=n;j++)if(e[i][j]&&subin(j,S))ok0=1;
			for(int j=1;j<=n;j++)if(e[j][i]&&subin(j,S))ok1=1;
			if(ok0&&ok1){fl=0;break;}
		}
		if(!fl)continue;
		fdp[0]=1;
		vi vec;
		for(int T=S;;T=(T-1)&S){
			vec.pb(T);
			if(T==0)break;
		}
		reverse(vec.begin(),vec.end());
		for(auto T:vec){
			for(int i=1;i<=n;i++)if(!subin(i,T)&&subin(i,S)&&!(fr[i]&T))
				cadd(fdp[T|bit(i-1)],fdp[T]);
		}
		f[S]=fdp[S];
		for(auto T:vec)fdp[T]=0;
	}
	g[0][0]=1;
	for(int S=1;S<bit(n);S++){
		for(int i=1;i<=n;i++){
			int lbt=S&(-S);
			for(int T=S;T;T=(T-1)&S)if(lbt&T){
				int A=T^S;
				if((frs[A]&T)||(frs[T]&A))continue;
				cadd(g[i][S],1ll*g[i-1][A]*f[T]%mod);
			}
		}
	}
	h[0][0]=1;
	for(int S=0;S<bit(n);S++){
		for(int i=0;i<n;i++)if(h[i][S]){
			for(int T=(S+1)|S;T<bit(n);T=(T+1)|S){
				int A=T^S;
				if(frs[S]&A)continue;
				for(int j=1;i+j<=n;j++)if(g[j][A]){
					if(j&1)cadd(h[i+j][T],1ll*h[i][S]*g[j][A]%mod);
					else cdel(h[i+j][T],1ll*h[i][S]*g[j][A]%mod);
				}
			}
		}
	}
	for(int len=1;len<=k+1&&len<=n;len++){
		cadd(ans,1ll*fac[len]*kcf[len]%mod*h[len][bit(n)-1]%mod);
	}
	int cnt=fac[n];
	for(int i=1;i<=k;i++)cnt=1ll*cnt*(n+i)%mod;
	dpi(ans,cnt);
	ans=1ll*ans*qpow(cnt,mod-2)%mod;
	cout<<ans<<'\n';
    #ifdef do_while_true
//		cerr<<'\n'<<"Time:"<<1.0*clock()/CLOCKS_PER_SEC*1000<<" ms"<<'\n';
	#endif
	return 0;
}