#include<bits/stdc++.h>
#define ll long long
#define ssz(x) ((int)x.size())
using namespace std;
const int N=1e6+5,eps=1e-4;
int n,m;
inline int red(){
	int data=0;bool w=0;char ch=getchar();
	while(ch!='-' && (ch<'0' || ch>'9'))ch=getchar();
	if(ch=='-') w=1,ch=getchar();
	while(ch>='0' && ch<='9') data=(data<<3)+(data<<1)+ch-'0',ch=getchar();
	return w?-data:data;
}
double len[N];
int x[N],y[N];
double s;
double dis(double x,double y){
	return x*x+y*y;
}
double ans=1000;
void calc(int l, int r, double nowl, double nowr, double det)
{
	if(det < eps) return;
	double vx1=x[l+1]-x[l],vy1=y[l+1]-y[l],vx2=x[r+1]-x[r],vy2=y[r+1]-y[r];
	double x1=x[l]+vx1*nowl/len[l],y1=y[l]+vy1*nowl/len[l];
	double x2=x[l]+vx1*(nowl+det)/len[l],y2=y[l]+vy1*(nowl+det)/len[l];
	double x3=x[r]+vx2*nowr/len[r],y3=y[r]+vy2*nowr/len[r];
	double x4=x[r]+vx2*(nowr+det)/len[r],y4=y[r]+vy2*(nowr+det)/len[r];
	x2 = x2-x1; y2 = y2-y1; x4 = x4-x3; y4 = y4-y3;
	double a=dis(x2-x4,y2-y4), b=2*((x2-x4)*(x1-x3)+(y2-y4)*(y1-y3)), c=dis(x1-x3,y1-y3);
	ans = min(ans,c); ans = min(ans,a+b+c);
	double s0 = -b/(2*a);
	if(s0 >= 0 && s0 <= 1) ans = min(ans,a*s0*s0+b*s0+c);
	//printf("nowans: %.9f\n",ans);
}
void solve(){
	scanf("%lf%d",&s,&n);
	for(int i=1;i<=n;i++){
		scanf("%d%d",&x[i],&y[i]);
	}
	for(int i=1;i<n;i++){
		len[i]=dis(x[i]-x[i+1],y[i]-y[i+1]);
		len[i] = sqrt(len[i]);
	}
	int l=1,r=1;
	double nowl=0,nowr=s;
	while(r<n&&nowr>=len[r]){
		nowr-=len[r];
		r++;
	}
	while(r<n){
		double det=min(len[l]-nowl,len[r]-nowr);
		calc(l,r,nowl,nowr,det);
		nowl+=det;
		nowr+=det;
		//printf("now: %d %d %.7f %.7f %.7f\n",l,r,nowl,nowr,det);
		if(nowl+eps>=len[l])nowl=0,l++;
		if(nowr+eps>=len[r])nowr=0,r++;
		//if(det < 1e-4) break;
	}
	printf("%.8f",sqrt(ans));
}
int main()
{
	//ios::sync_with_stdio(false);
	//cin.tie(0);
	//cout.tie(0); 
	int T=1;
	while(T--)solve();
	return 0;
}