/*
in the name of god
*/
//#pragma GCC optimize("Ofast,O3,unroll-loops")
//#pragma GCC target("avx,avx2,fma")
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4.1,sse4.2,sse4a,avx,avx2,popcnt,tune=native")
#include <bits/stdc++.h>
using namespace std;
#define int long long
typedef pair<int,int> pii;
typedef pair<long long ,long long> pll;
typedef long long ll ;
#define File freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout);
#define all(V) V.begin(),V.end()
#define setprec(x) fixed << setprecision(x)
#define Mp(a,b) make_pair(a,b)
#define len(V) (int)(V.size())
#define sep ' '
#define endl '\n'
#define pb(x) push_back(x)
#define fi first
#define sec second
#define popcount(x) __builtin_popcount(x)
#define lid u<<1
#define rid (lid)|1
mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());
const ll N = 2e5 + 10,SQ=320,LOG=31;
const ll inf = 2e9 , MD = 1e9 + 7;
inline ll md(ll x){ x %= MD; return (x < 0 ? x + MD : x);}
int n , m;
int par[N];
void DSU(){
iota(par+1,par+n+1,1);
}
int getpar(int u){
return (par[u] == u ? u : par[u] = getpar(par[u]));
}
void merge(int u,int v){
u=getpar(u),v=getpar(v);
if(u==v) return;
par[u] = v;
}
pii E[N];
bool mark[N];
int dis[N];
int pr[N];
vector<int> g[N];
vector<int> sub[N];
void dfs(int u,int p){
mark[u] = 1;
pr[u] = p;
dis[u] = dis[p] + 1;
for(auto h : g[u]){
if(!mark[h]) dfs(h,u);
else if(dis[h] < dis[u] and h != p){
int v = u;
while(v != h){
merge(v,pr[v]);
v = pr[v];
}
}
}
}
int dp[N];
int tmp[N];
int ps[N];
int P[N];
int H[N];
void dfs2(int u,int p){
P[u] = p;
int head = -1;
for(auto h : sub[u]){
for(auto x : g[h]){
if(pr[x] != p and pr[x] != u) dfs2(pr[x],u);
if(pr[x] == p ) head = h;
}
}
H[u] = head;
if(len(sub[u]) == 1){
dp[u] = 1;
for(auto h : g[sub[u][0]]){
if(pr[h] != p) dp[u] = md(dp[u] * md(dp[pr[h]] + 1));
}
return;
}
//cout << u << " -- " << head << endl;
//for(auto h : sub[u]) cout << h << sep;
//cout << endl;
if(head != -1){
for(auto h : sub[u]){
tmp[h] = 1;
for(auto x : g[h]){
if(pr[x] != p and pr[x] != u) tmp[h] = md(tmp[h] * md(dp[pr[x]]+1));
}
//cout << tmp[h] << sep;
}
//cout << endl;
int tot = 1;
for(auto h : sub[u]) tot = md(tot * tmp[h]);
int z = 1;
ps[sub[u][0]] = 0;
for(auto h : sub[u]){
z = md(z * tmp[h]);
ps[sub[u][0]] = md(ps[sub[u][0]] + z);
}
ps[sub[u][0]] = md(ps[sub[u][0]] - tot);
for(int i = len(sub[u]) - 1;i > 0;i--){
int nxt = (i+1)%len(sub[u]);
ps[sub[u][i]] = md(tmp[sub[u][i]] * md(1 + ps[sub[u][nxt]]));
ps[sub[u][i]] = md(ps[sub[u][i]] - tot);
}
dp[u] = 0;
//for(auto h : sub[u]) cout << ps[h] << sep;
//cout << endl;
for(auto h : sub[u]) dp[u] = md(dp[u] + ps[h]);
int ind ;
for(int i = 0;i < len(sub[u]);i++){
if(sub[u][i] == head) ind = i;
}
ind = (ind + 1)%len(sub[u]);
vector<int> bad;
for(int i = ind;;i = (i+1)%len(sub[u])){
if(sub[u][i] == head) break;
bad.pb(sub[u][i]);
}
int d = 0;
//cout << "bad" << endl;
//for(auto h : bad) cout << h << sep;
//cout << endl;
for(auto h : bad){
d = md(tmp[h] * md(d+1));
dp[u] = md(dp[u] - d);
}
}
}
int32_t main() {
ios_base::sync_with_stdio(false);cout.tie(0);cin.tie(0);
cin >> n >> m;
for(int i =1 ;i<=m;i++){
cin >> E[i].fi >> E[i].sec;
if(E[i].sec < E[i].fi) swap(E[i].fi,E[i].sec);
g[E[i].fi].pb(E[i].sec);
g[E[i].sec].pb(E[i].fi);
}
DSU();
dfs(1,1);
vector<int> st;
for(int i = 1;i<=n;i++){
st.pb(getpar(i));
}
sort(all(st));
st.resize(unique(all(st)) - st.begin());
for(int i = 1;i<=n;i++){
int v = lower_bound(all(st),getpar(i)) - st.begin() + 1;
pr[i] = v;
sub[v].pb(i);
}
for(int i =1 ;i <= len(st);i++){
sort(all(sub[i]),[&](int u,int v){return dis[u] < dis[v];});
}
dfs2(pr[1],0);
int ans = 0;
//for(int i =1 ;i<=len(st);i++) cout << dp[i] << sep;
//cout << endl;
for(int u = 1;u<=len(st);u++){
if(len(sub[u]) == 1) ans = md(ans + dp[u]);
else{
for(auto h : sub[u]){
tmp[h] = 1;
for(auto x : g[h]){
if(pr[x] != P[u] and pr[x] != u) tmp[h] = md(tmp[h] * md(dp[pr[x]]+1));
}
}
//cout << u << " | ";
//for(auto h : sub[u]) cout << tmp[h] << sep;
//cout << endl;
int tot = 1;
for(auto h : sub[u]) tot = md(tot * tmp[h]);
int z = 1;
//cout << tot << endl;
ps[sub[u][0]] = 0;
for(auto h : sub[u]){
z = md(z * tmp[h]);
ps[sub[u][0]] = md(ps[sub[u][0]] + z);
}
//cout << ps[sub[u][0]] << endl;
ps[sub[u][0]] = md(ps[sub[u][0]] - tot);
for(int i = len(sub[u]) - 1;i > 0;i--){
int nxt = (i+1)%len(sub[u]);
ps[sub[u][i]] = md(tmp[sub[u][i]] * md(1 + ps[sub[u][nxt]]));
ps[sub[u][i]] = md(ps[sub[u][i]] - tot);
//cout << ps[sub[u][i]] << sep;
}
//cout << endl;
for(auto h : sub[u]) ans = md(ans + ps[h]);
}
}
cout << ans << endl;
return 0;
}
