#include<bits/stdc++.h>
#define ll long long
#define N 500005
#define mod 1000000007ll
using namespace std;
struct node{
    ll t,n;
}edge[N<<2];
ll head[N],cn=-1,n,m,dfn[N],low[N],cnt=0,nt=0,ji[N],siz[N],dp[N][2],er[N<<1],e[N],sum[N],ans;
bool vis[N];
stack<ll>s;
vector<ll>v[N];
ll read(){char c=getchar();
    ll n=0;
    while(c<'0'||c>'9')c=getchar();
    while(c<='9'&&c>='0')n=(n<<1)+(n<<3)+c-'0',c=getchar();
    return n;
}
void add(ll a,ll b){
    edge[++cn]={b,head[a]};
    head[a]=cn;
}
void tarjan(ll f,ll la){
    dfn[f]=low[f]=++cnt,s.push(f),vis[f]=true;
    for(auto i:v[f]){
        if(i==la)continue;
        if(!dfn[i])tarjan(i,f),low[f]=min(low[f],low[i]);
        else if(vis[i])low[f]=min(low[f],dfn[i]);
    }
    if(dfn[f]==low[f]){ll t;nt++;
        do{
            t=s.top(),s.pop();
            ji[t]=nt,siz[nt]++,vis[t]=false;
        }while(t!=f);
    }
}
//dp[i][1/0]表示第i个点，强制选到i，子树内有无军营
void dfs(ll f,ll la){ll i;
    dp[f][0]=er[e[f]],dp[f][1]=(er[e[f]+siz[f]]-er[e[f]]+mod)%mod;
    for(i=head[f];i!=-1;i=edge[i].n){
        if(edge[i].t==la)continue;
        dfs(edge[i].t,f);
        dp[f][1]=(dp[f][0]*dp[edge[i].t][1]%mod+dp[f][1]*(dp[edge[i].t][0]*2+dp[edge[i].t][1])%mod)%mod;
        dp[f][0]=dp[f][0]*dp[edge[i].t][0]*2%mod;
    }
    if(f==1)ans=(ans+dp[f][1])%mod;
    else ans=(ans+dp[f][1]*er[sum[1]-sum[f]-1]%mod)%mod;
}
void dfs1(ll f,ll la){sum[f]=e[f];
    for(ll i=head[f];i!=-1;i=edge[i].n){
        if(edge[i].t==la)continue;
        dfs1(edge[i].t,f);
        sum[f]+=sum[edge[i].t]+1;
    }
}
int main(){ll i,k,x,y;
    memset(head,-1,sizeof(head));
    n=read(),m=read();
    for(i=1;i<=m;i++){x=read(),y=read();
        v[x].push_back(y),v[y].push_back(x);
    }
    tarjan(1,0);er[0]=1;
    for(i=1;i<=n+m;i++)er[i]=er[i-1]*2ll%mod;
    for(i=1;i<=n;i++){
        for(auto k:v[i]){
            if(ji[k]!=ji[i])add(ji[k],ji[i]);
            else e[ji[i]]++;
        }
    }
    for(i=1;i<=nt;i++)e[i]>>=1;
    dfs1(1,0);
    dfs(1,0);
    cout<<ans;
}