#include<bits/stdc++.h>
#define ll long long
using namespace std;
inline int read(){
	int s = 0;char ch = getchar();
	while(ch<'0'||ch>'9')ch = getchar();
	while(ch>='0'&&ch<='9'){s = (s<<1)+(s<<3)+ch-'0';ch = getchar();}
	return s;
}
mt19937_64 rd(time(0));
const int N = 200005,md = 1e9+7;
int hd[N],ect = 2,n,m,dfn[N],ct,kct;
ll sum[N],hsum[N],esum;
struct E{
	int v,nt;
	bool ite;
}e[2*N];
void add(int u,int v){
	e[ect].ite = 0;
	e[ect].v = v;
	e[ect].nt = hd[u];
	hd[u] = ect++;
}
map<ll,int> hc;
int hct;
void tarjan(int p,int lt){
	dfn[p] = ++ct;
	int v;
	for(int i = hd[p];i;i = e[i].nt){
		if(i==(lt^1))continue;
		v = e[i].v;
		if(!dfn[v]){
			e[i].ite = 1;
			tarjan(v,i);
		}else if(i&1){
			ll nrd = rd();
			sum[v]^=nrd;sum[p]^=nrd;
			if(!hc[nrd])hc[nrd] = ++hct,hsum[hct] = 0;
			hsum[hc[nrd]]++;
			esum++;
		}
	}
}
void dfs(int p){
	for(int i = hd[p];i;i = e[i].nt){
		if(!e[i].ite)continue;
		dfs(e[i].v);
		sum[p]^=sum[e[i].v];
		if(!sum[e[i].v])continue;
		esum++;
		if(!hc[sum[e[i].v]]){
			hc[sum[e[i].v]] = ++hct;
			hsum[hct] = 0;
		}
		hsum[hc[sum[e[i].v]]]++;
	}
}
ll fp(int p){
	ll x = 2,ans = 1;
	while(p){
		if(p&1)ans = ans*x%md;
		x = x*x%md;
		p>>=1;
	}
	return ans;
}
int main(){
	ll iv = fp(md-2);ll iiv = iv*iv%md;
	while(scanf("%d%d",&n,&m)>0){
		int u,v;
		hc.clear();
		ect = 2;kct = 0;hct = 0;esum = 0;ct = 0;
		for(int i = 1;i<=n;i++)dfn[i] = sum[i] = hd[i] = 0;
		for(int i = 1;i<=m;i++){
			u = read();v = read();
			add(u,v);add(v,u);
		}
		for(int i = 1;i<=n;i++){
			if(!dfn[i]){
				tarjan(i,0);
				kct++;
				dfs(i);
			}
		}
		ll ans = 0;
		for(int i = 1;i<=hct;i++){
			ans+=hsum[i]*hsum[i]%md*iv%md+(esum-hsum[i])*hsum[i]%md*iiv%md;
			ans%=md;
		}
		printf("%lld\n",ans*fp(m-n+kct)%md);
	}
	return 0;
}