#include <bits/stdc++.h>
using namespace std;
typedef long long int ll;
typedef long double ld;
#define pb push_back
#define pf push_front
#define fi first
#define se second
const ll mod = 1e9+7, mxn = 1e5+7;
ll n, m, pr[mxn], dp[mxn][2], mul[mxn<<1];
bool ck[mxn], vis[mxn];
vector<ll> cycle;
vector<vector<ll>> g(mxn);
void get_cycle(ll u, ll v)
{
// cerr << u << '\n';
cycle.pb(u); ck[u] = 1;
if (u == v) return;
get_cycle(pr[u],v);
}
void dfs(ll u, ll v)
{
vis[u] = 1;
for (ll i : g[u]) if (i != v)
{
if (vis[i] && !cycle.size())
{
// cerr << u << ' ' << i << '\n';
get_cycle(u,i);
}
else if (!vis[i])
{
pr[i] = u;
dfs(i,u);
}
}
}
void dfs_dp(ll u, ll v)
{
dp[u][1] = 1;
for (ll i : g[u]) if (i != v && !ck[i])
{
dfs_dp(i,u);
dp[u][1] *= dp[i][1]+1;
dp[u][1] %= mod;
dp[u][0] += (dp[i][0]+dp[i][1])%mod;
if (dp[u][0] >= mod) dp[u][0] -= mod;
}
}
ll bpow(ll a, ll b)
{
if (!b) return 1;
ll m = bpow(a,b/2);
if (b&1) return (((m*m)%mod)*a)%mod;
return (m*m)%mod;
}
signed main()
{
ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
// freopen("test.inp","r",stdin); freopen("test.out","w",stdout); freopen("test.err","w",stderr);
cin >> n >> m;
for (ll i = 1; i <= m; i++)
{
ll a, b; cin >> a >> b;
g[a].pb(b); g[b].pb(a);
}
dfs(1,1);
if (!cycle.size()) cycle.pb(1);
for (ll i : cycle) dfs_dp(i,i);
ll ans = 0, id = 0; mul[0] = 1;
for (ll i : cycle)
{
ans += (dp[i][0]+dp[i][1])%mod;
if (ans >= mod) ans -= mod;
id++; mul[id] = dp[i][1];
}
n = cycle.size();
for (ll i = n+1; i <= 2*n; i++) mul[i] = mul[i-n];
for (ll i = 1; i <= 2*n; i++) mul[i] = (mul[i]*mul[i-1])%mod;
queue<ll> q;
ll s = 0;
for (ll i = 0; i < n-1; i++)
{
ll inv = bpow(mul[i],mod-2);
q.push(inv); s += inv;
if (s >= mod) s -= mod;
}
for (ll i = n-1; i <= 2*n-2; i++)
{
ans += (s*mul[i])%mod;
if (ans >= mod) ans -= mod;
s -= q.front();
if (ans < 0) ans += mod;
ll inv = bpow(mul[i-2],mod-2);
q.push(inv); s += inv;
if (s >= mod) s -= mod;
}
cout << ans;
}
