#include <bits/stdc++.h>

#define i64 long long
#define ui64 unsigned i64
#define all(x) x.begin(), x.end()
#define seg(a, l, r) a + l, a + r + 1
#define rep(i, a, b) for(int i = (a); i <= (b); i++)
#define per(i, a, b) for(int i = (a); i >= (b); i--)

using namespace std;

const int N = 1e6 + 5, MOD = 1e9 + 7;

mt19937_64 mt_rand(chrono::system_clock::now().time_since_epoch().count()); 

struct Edge {
    int u, v, nxt;

    Edge() {}
    Edge(int _u, int _v, int _nxt) {
        u = _u; v = _v; nxt = _nxt;
    }
} E[N << 1];

int n, m, c, tot;
int pw2[N], head[N];
ui64 s[N << 1], val[N << 1];
bool vis[N]; 

void addEdge(int u, int v) {
    E[tot] = Edge(u, v, head[u]);
    head[u] = tot++;
}

void dfs(int u, int last) {
    vis[u] = true;

    for(int i = head[u]; ~i; i = E[i].nxt) {
        int v = E[i].v;
        if(i == (last ^ 1)) continue;

        if(!vis[v]) {
            dfs(v, i);
            val[i / 2] = s[v];
            s[u] ^= s[v];
        }
        else if(val[i / 2] == 0) {
            val[i / 2] = mt_rand() + 1;
            s[u] ^= val[i / 2];
            s[v] ^= val[i / 2];
        }
    }
}

int main() {

    // freopen("fish.in", "r", stdin);
    // freopen("fish.out", "w", stdout);

    ios::sync_with_stdio(false);
    cin.tie(nullptr); cout.tie(nullptr);

    while (cin >> n >> m) {
        c = 0; tot = 0;
        memset(head, -1, sizeof(head));
        memset(vis, 0, sizeof(vis));
        memset(s, 0, sizeof(s));
        memset(val, 0, sizeof(val));
        rep(i, 1, m) {
            int u, v; cin >> u >> v;
            addEdge(u, v);
            addEdge(v, u);
        }

        pw2[0] = 1;
        rep(i, 1, m) pw2[i] = pw2[i - 1] * 2 % MOD;

        rep(i, 1, n) if(!vis[i]) dfs(i, 0), c++;

        int cnt = 0; // 非割边条数
        rep(i, 0, m - 1) if(val[i] > 0) cnt++;

        i64 ans = 1ll * cnt * pw2[m - n + c - 1] % MOD;

        sort(seg(val, 0, m - 1));
        for(int l = 0, r = 0; l < m; l = r + 1) {
            r = l;
            while(val[r + 1] == val[l]) r++;

            if(val[l] != 0) {
                int len = r - l + 1;
                ans = (ans + 1ll * len * (len - 1) % MOD * pw2[m - n + c - 1] % MOD) % MOD;
                ans = (ans + 1ll * len * (cnt - len) % MOD * pw2[m - n + c - 2] % MOD) % MOD;
            }
        }

        cout << ans << "\n";
    }

    return 0;
}