#include <bits/stdc++.h>
using namespace std;

typedef long double ld;

struct vec2{
  ld x=0,y=0;

  ld length()const{
    return hypotl(x,y);
  }

  vec2 operator-(vec2 const &a)const{
    return {x-a.x,y-a.y};
  }

  vec2 operator+(vec2 const &a)const{
    return {x+a.x,y+a.y};
  }

  vec2 operator*(ld const a)const{
    return {x*a,y*a};
  }

  vec2 operator/(ld const a)const{
    return {x/a,y/a};
  }
};

vector<vec2> v;
vector<ld> where;
ld dist;

vec2 pat(ld t){
  auto it=upper_bound(where.begin(),where.end(),t);
  if (it==where.begin()){
    return v.front();
  }
  if (it==where.end()){
    return v.back();
  }
  int i=(it-where.begin())-1;

  vec2 dirn=(v[i+1]-v[i]);
  dirn=dirn/dirn.length();
  return v[i]+dirn*(t-where[i]);
}

ld dat(ld t){
  vec2 a=pat(t);
  vec2 b=pat(t-dist);
  return (b-a).length();
}

int main(){
  cin>>dist;
  int n; cin>>n;
  v.resize(n); for (auto &i: v) cin>>i.x>>i.y;
  where.resize(n);

  vector<ld> key_times;
  {
    for (int i=0; i<n; i++){
      if (i) where[i]=where[i-1]+(v[i]-v[i-1]).length();
      key_times.push_back(where[i]);
      key_times.push_back(where[i]+dist);
    }
  }
  sort(key_times.begin(),key_times.end());

  ld res=dist;

  for (int i=1; i<key_times.size(); i++){
    if (dist<=key_times[i] and key_times[i]<=where.back()+1e-12L){
      ld lef=max(key_times[i-1],dist);
      ld rgt=key_times[i];

      for (int z=100; z--;){
        ld a=(lef*2+rgt)/3;
        ld b=(lef+rgt*2)/3;
        if (dat(a)<dat(b)){
          rgt=b;
        }else{
          lef=a;
        }
      }

      res=min(res,dat(lef));
    }
  }

  cout.precision(10);
  cout<<fixed<<res<<endl;
}