#include<bits/stdc++.h>
#define mod 1000000007
using namespace std;
int powdv(int x,int y=mod-2){
	int ans=1;
	while(y){
		if(y&1)ans=1ll*ans*x%mod;
		y>>=1,x=1ll*x*x%mod;
	}
	return ans;
}
int n,m,k;
int u[155],v[155];
int z1[1<<15],ct[1<<15];
bitset<25>mp[25];
bitset<125>b1[1<<15],b2[1<<15];
int gl[25],C[35][35];
int di[25];
int mb[1<<15];
struct pol{
	int a[16];
}jb,bj;
pol operator+(pol a,pol b){
	pol c;
	for(int i=0;i<=n;++i)c.a[i]=(a.a[i]+b.a[i])%mod;
	return c;
}
pol operator-(pol a,pol b){
	pol c;
	for(int i=0;i<=n;++i)c.a[i]=(a.a[i]-b.a[i]+mod)%mod;
	return c;
}
pol operator*(pol a,pol b){
	pol c;
	for(int i=0;i<=n;++i)c.a[i]=1ll*a.a[i]*b.a[i]%mod;
	return c;
}
pol operator*(int a,pol b){
	pol c;
	for(int i=0;i<=n;++i)c.a[i]=1ll*a*b.a[i]%mod;
	return c;
}
pol f[1<<15],h[1<<15];
int y[25];
int a1[25],a2[25];
int main(){
	scanf("%d%d%d",&n,&m,&k);
	for(int i=0;i<=2*n+1;++i){
		C[i][0]=1;
		for(int j=1;j<=i;++j){
			C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod;
		}
	}
	di[0]=1;
	for(int i=1;i<=n;++i)di[i]=1ll*i*di[i-1]%mod;
	int pd=powdv(C[n+k][n]);
	for(int i=0;i<n&&i<=k;++i){
		gl[i]=1ll*1*C[k+1][i+1]%mod*pd%mod;
	}
	for(int i=1;i<=m;++i){
		scanf("%d%d",&u[i],&v[i]);
		mp[u[i]][v[i]]=1;
	}
	for(int i=1;i<(1<<n);++i){
		for(int j=1;j<=m;++j){
			int A=(i>>(u[j]-1))&1,B=(i>>(v[j]-1))&1;
			if(A)b1[i][j]=1,mb[i]|=1<<(v[j]-1);
			if(B)b2[i][j]=1;
		}
	}
	z1[0]=1;
	for(int i=0;i<(1<<n);++i)for(int j=1;j<=n;++j){
		if(i&(1<<(j-1)))continue;
		int fl=1;
		for(int k=1;k<=n;++k)if(mp[k][j]&&((i>>(k-1))&1))fl=0;
		if(fl)z1[i^(1<<(j-1))]=(z1[i^(1<<(j-1))]+z1[i])%mod;
	}
	for(int i=0;i<(1<<n);++i)ct[i]=__builtin_ctz(i);
	for(int i=0;i<=n;++i)jb.a[i]=i,bj.a[i]=1;
	int ans=0;
	h[0]=bj;
	for(int i=1;i<(1<<n);++i)for(int j=i;j;j=(j-1)&i){
		if(!(mb[j]&(i^j))&&!(mb[i^j]&j)&&ct[j]==ct[i]){
			h[i]=h[i]-h[i^j]*(z1[j]*jb);
		}
	}
	f[0]=bj;
	for(int i=1;i<(1<<n);++i){
		for(int j=i;j;j=(j-1)&i){
			if(!(mb[i^j]&j))f[i]=f[i]-h[j]*f[i^j];
		}
	}
	for(int i=0;i<=n;++i)y[i]=f[(1<<n)-1].a[i];
	for(int i=0;i<=n;++i){
		int cj=y[i];
		for(int j=0;j<=n;++j)a2[j]=0;
		a2[0]=1;
		int ss=0;
		for(int j=0;j<=n;++j)if(j!=i){
			cj=1ll*cj*powdv(i-j+mod)%mod;
			for(int k=ss;k>=0;--k){
				a2[k+1]=(a2[k+1]+a2[k])%mod;
				a2[k]=1ll*(mod-j)*a2[k]%mod;
			}
			++ss;
		}
		for(int j=0;j<=n;++j)a1[j]=(a1[j]+1ll*cj*a2[j])%mod;
	}
	for(int i=0;i<n&&i<=k;++i){
		ans=(ans+1ll*di[i+1]*a1[i+1]%mod*gl[i])%mod;
	}
	int nj=1;
	for(int i=1;i<=n;++i)nj=1ll*nj*i%mod;
	ans=1ll*ans*powdv(nj)%mod;
	ans=(ans+mod)%mod;
	printf("%d\n",ans);
	return 0;
}