#include <bits/stdc++.h>
using namespace std;
int n , m;
vector<int> E[200005];
bool vis[200005];
// int dis[200005];
double ans[200005];
double pre[200005];
vector<double> ag[200005];
typedef pair<double,int> pdi;
double tr[200005];
int main() {
    ios::sync_with_stdio(false) ; cin.tie(0) ; cout.tie(0) ;
    cin >> n >> m;
    for(int i = 1;i <= m;i++) {
        int u , v;cin >> u >>v;
        E[u].push_back(v) ; E[v].push_back(u);
    }
    tr[0] = 1;
    for(int i = 1;i <= n;i++) tr[i] = tr[i - 1] / 4;

    for(int i = 1;i <= n;i++) ans[i] = 1e9;
    ans[n] = 0.0;
    priority_queue<pdi , vector<pdi> , greater<pdi> > pq;
    pq.push({ans[n] , n}) ;
    while(pq.size()) {
        auto u = pq.top().second ; pq.pop() ;
        if(vis[u]) continue ;
        vis[u] = 1;
        for(auto v : E[u]) {
            ag[v].push_back(ans[u]) ;
            pre[v] += 0.75 * tr[(int)ag[v].size() - 1] * (ans[u] + (int)ag[v].size());
            double sol = pre[v] +  + tr[ag[v].size()] * (ag[v][0] + (int)ag[v].size() + 2);
            // printf("%d %lf\n",v,sol) ;
            if(sol < ans[v]) {
                ans[v] = sol;
                pq.push({ans[v] , v});
            }
        }
    }
    printf("%.12lf\n",ans[1]) ;
}