#include <bits/stdc++.h>

using namespace std;

#define FOR(i, a, b) for(int i = (a); i < (b); i++)
#define RFOR(i, a, b) for(int i = (a) - 1; i >= (b); 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 long double db;

struct Pt
{
	db x, y;
	Pt operator+(const Pt& p) const
	{
		return {x + p.x, y + p.y};
	}
	Pt operator-(const Pt& p) const
	{
		return {x - p.x, y - p.y};
	}
	Pt operator*(db d) const
	{
		return {x * d, y * d};
	}
	Pt operator/(db d) const
	{
		return {x / d, y / d};
	}
};
db sq(const Pt& p)
{
	return p.x * p.x + p.y * p.y;
}
db abs(const Pt& p)
{
	return sqrt(sq(p));
}
ostream& operator<<(ostream& os, const Pt& p)
{
	return os << "(" << p.x << "," << p.y << ")";
}
const db phi = (3. - sqrt(5.0)) / 2.;

db f(Pt a, Pt b, Pt c, Pt d)
{
	Pt vec1 = b - a;
	Pt vec2 = d - c;
	
	//cerr << "TER:\n";
	//cerr << a << b << c << d << '\n';
	
	db L = 0, R = abs(b - a);	
	db M1, M2, v1, v2;
	M1 = L + (R - L) * phi;
	M2 = R - (R - L) * phi;
	v1 = abs((a + vec1 * M1) - (c + vec2 * M1));
	v2 = abs((a + vec1 * M2) - (c + vec2 * M2));
	FOR (i, 0, 74)
	{
 	   	if (v1 > v2) // for minimum
		{
			L = M1;
			M1 = M2;
			v1 = v2;
			M2 = R - (R - L) * phi;
			v2 = abs((a + vec1 * M2) - (c + vec2 * M2));
		}
		else
		{
			R = M2;
			M2 = M1;
			v2 = v1;
			M1 = L + (R - L) * phi;
			v1 = abs((a + vec1 * M1) - (c + vec2 * M1));
		}
	}
	return abs((a + vec1 * L) - (c + vec2 * L));
}

int main()
{
	ios::sync_with_stdio(0); 
	cin.tie(0);
	cout << fixed << setprecision(7 + 7 + 7);
	
	db s;
	cin >> s;
	int n;
	cin >> n;
	vector<Pt> a(n);
	FOR (i, 0, n)
		cin >> a[i].x >> a[i].y;
	
	int idx1 = 1;
	int idx2 = 1;
	Pt p1 = a[0];
	Pt p2 = a[0];
	db need = s;
	FOR (i, 1, n)
	{
		db d = abs(a[i] - a[i - 1]);
		if (d < need)
			need -= d;
		else
		{
			Pt v = a[i] - a[i - 1];
			p2 = a[i - 1] + v / d * need;
			idx2 = i;
			break;
		}
	}
	db ans = abs(p2 - p1);
	while (idx2 < n)
	{
		db d1 = abs(a[idx1] - p1);
		db d2 = abs(a[idx2] - p2);
		if (d1 < d2)
		{
			Pt p = a[idx2] - a[idx2 - 1];
			db d = abs(p);
			Pt end = p2 + (p / d * d1);
			ans = min(ans, f(p1, a[idx1], p2, end));
			p1 = a[idx1];
			p2 = end;
			idx1++;
		}
		else
		{
			Pt p = a[idx1] - a[idx1 - 1];
			db d = abs(p);
			Pt end = p1 + (p / d * d2);
			ans = min(ans, f(p1, end, p2, a[idx2]));
			p2 = a[idx2];
			p1 = end;
			idx2++;			
		}
	}
	cout << ans << '\n';
	return 0;
}