#include <bits/stdc++.h>
#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
const int inf = 1000000007;
const long long linf = 1LL << 62;
const unsigned long long ulinf = 1ULL << 63;
const double eps = 0.000001;
const double pi = 3.14159265358979323846;
template <class T>
T abs(T a) {
  return a >= 0 ? a : -a;
}
template <class T>
T sqr(T a) {
  return a * a;
}
template <class T>
T gcd(T a, T b) {
  return b ? gcd(b, a % b) : a;
}
template <class T>
T mod(T a, T b) {
  return (a % b + b) % b;
}
long long powmod(long long a, long long b, long long c) {
  if (b == 0LL) return 1LL;
  long long ret = powmod(a, b >> 1, c);
  ret = ret * ret % c;
  if (b & 1LL) ret = ret * a % c;
  return ret;
}
long long inv(long long a, long long b) { return powmod(a, b - 2LL, b); }
template <class T>
void maxe(T &a, T b) {
  if (a < b) a = b;
}
template <class T>
void mine(T &a, T b) {
  if (a > b) a = b;
}
int iszero(double a) { return abs(a) <= eps; }
template <class T>
void geti(T &a) {
  a = 0;
  T b = 1;
  char c = getchar();
  if (c == '-')
    b = -1;
  else
    a = c - 48;
  while ((c = getchar()) != ' ' && c != '\n') a = a * 10 + c - 48;
  a *= b;
}
void fileio_in_out() {
  freopen(".in", "r", stdin);
  freopen(".out", "w", stdout);
}
void fileio_txt() {
  freopen("input.txt", "r", stdin);
  freopen("output.txt", "w", stdout);
}
const int N = 111;
const int M = 155555;
const int K = 20;
int test;
int n, m, k;
long long ans;
vector<int> v[N];
int vis[N];
long long d1[N], cnt1[N], d2[N], cnt2[N];
void dijk(int s, long long d[], long long cnt[]) {
  for (int i = 0; i <= n; i++) {
    d[i] = inf;
    vis[i] = 0;
  }
  d[s] = 0;
  cnt[s] = 1;
  while (1) {
    int x = 0;
    for (int i = 1; i <= n; i++)
      if (!vis[i] && d[i] < d[x]) x = i;
    if (!x) return;
    vis[x] = 1;
    for (int i = 0; i < v[x].size(); i++) {
      int y = v[x][i];
      if (d[y] > d[x] + 1) {
        d[y] = d[x] + 1;
        cnt[y] = cnt[x];
      } else {
        if (d[y] == d[x] + 1) cnt[y] += cnt[x];
      }
    }
  }
}
int main() {
  scanf("%d%d", &n, &m);
  for (int i = 1; i <= m; i++) {
    int x, y;
    scanf("%d%d", &x, &y);
    v[x].push_back(y);
    v[y].push_back(x);
  }
  dijk(1, d1, cnt1);
  dijk(n, d2, cnt2);
  for (int i = 1; i <= n; i++)
    if (d1[i] + d2[i] == d1[n]) {
      long long t = (i == 1 || i == n) ? 1 : 2;
      t *= cnt1[i] * cnt2[i];
      maxe(ans, t);
    }
  printf("%.10lf\n", 1.0 * ans / cnt1[n]);
  return 0;
}
