#include<bits/stdc++.h>
using namespace std;
int n,m,f[200010];
vector<int> a[200010],v[200010];
__float128 d[200010];
void solve(int x){
	__float128 z=0,k=1e9,p=1;
	for(int i=0;i<a[x].size();i++){
		int y=a[x][i];
		z+=0.75*p*(d[y]+i+1);
		p*=0.25;
		k=min(k,z+(d[a[x][0]]+i+3)*p);
		if(i>30) break;
	}
	d[x]=k;
}
int main(){
	priority_queue<pair<__float128,int> > q;
	int x,y;
	cin>>n>>m;
	for(int i=1;i<=m;i++){
		cin>>x>>y;
		v[x].push_back(y);
		v[y].push_back(x);
	}
	d[n]=0;
	q.push(make_pair(0,n));
	while(!q.empty()){
		int x=q.top().second; q.pop();
		if(f[x]) continue;
		f[x]=1;
		for(int i=0;i<v[x].size();i++){
			int y=v[x][i];
			a[y].push_back(x);
			solve(y);
			q.push(make_pair(-d[y],y));
		}
	}
	printf("%.9lf",(double)d[1]);
	return 0;
}