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

#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define RFOR(i, b, a) for(int i = (b) - 1; i >= (a); i--)
#define SZ(a) (int)a.size()
#define ALL(a) a.begin(), a.end()
#define PB push_back
#define MP make_pair
#define F first
#define S second

typedef long long LL;
typedef vector<int> VI;
typedef pair<int, int> PII;
typedef double db;

struct pt
{
	db x, y;
	pt() {}
	pt(db _x, db _y) : x(_x), y(_y) {}
	
	
	pt operator+(const pt p) const
	{
		return pt(x + p.x, y + p.y);
	}
	pt operator-(const pt p) const
	{
		return pt(x - p.x, y - p.y);
	}
	pt operator*(db coef) const
	{
		return pt(x * coef, y * coef);
	}
	db len()
	{
		return sqrt(x * x + y * y);
	}
	pt scale(db val)
	{
		return *this * (val / len());
	}
};

const int N = 1 << 20;
pt p[N];
db t[N]; //p[i] -> p[i + 1] start in t[i]
db s;

db val(int i0, int i1, db m)
{
	pt p0 = p[i0] + (p[i0 + 1] - p[i0]).scale(m - t[i0]);
	pt p1 = p[i1] + (p[i1 + 1] - p[i1]).scale(s + m - t[i1]);
	return (p0 - p1).len();
}

db find(int i0, int i1, db tL, db tR)
{
	FOR(it, 0, 70)
	{
		db m1 = (tL * 2 + tR) / 3;
		db m2 = (tR * 2 + tL) / 3;
		
		if(val(i0, i1, m1) > val(i0, i1, m2))
			tL = m1;
		else
			tR = m2;
	}
	return val(i0, i1, tL);
} 



int main()
{
    ios::sync_with_stdio(0); 
    cin.tie(0);
    int n;
    cin >> s >> n;
    FOR(i, 0, n)
		cin >> p[i].x >> p[i].y;
	FOR(i, 0, n - 1)
	{
		t[i + 1] = t[i] + (p[i + 1] - p[i]).len();
	}
	vector<pair<db, int>> events;
	FOR(i, 1, n)
	{
		//t + s;
		events.PB(MP(t[i] - s, 1)); 
		events.PB(MP(t[i], 0));
	}
	sort(ALL(events));
	db ans = s;
	int i0 = 0, i1 = 0;
	db prevT = 0;
	for(auto [time, ind] : events)
	{
		if(time > 0)
		{
			ans = min(ans, find(i0, i1, prevT, time));
			//cout << i0 << " " << i1 << " " << prevT << " " << time << endl;
			
			
			prevT = time;
		}
		if(ind == 1)
			i1++;
		else
			i0++;
		if(i1 == n - 1 || i0 == n - 1)
			break;
	}
	cout << fixed << setprecision(10) << ans << endl;
	
	
	

	return 0;
}