#include <iostream>
#include <vector>
#include <cmath>
#include <functional>
#include <iomanip>
using namespace std;
using ld = long double;
using pld = pair<ld,ld>;
using pii = pair<int, int>;
const ld eps = 1e-9;

template <class T> int sgn(T x) { return (x > 0) - (x < 0); }
template<class T>
struct Point {
	typedef Point P;
	T x, y;
	explicit Point(T x=0, T y=0) : x(x), y(y) {}
	bool operator<(P p) const { return tie(x,y) < tie(p.x,p.y); }
	bool operator==(P p) const { return tie(x,y)==tie(p.x,p.y); }
	P operator+(P p) const { return P(x+p.x, y+p.y); }
	P operator-(P p) const { return P(x-p.x, y-p.y); }
	P operator*(T d) const { return P(x*d, y*d); }
	P operator/(T d) const { return P(x/d, y/d); }
	T dot(P p) const { return x*p.x + y*p.y; }
	T cross(P p) const { return x*p.y - y*p.x; }
	T cross(P a, P b) const { return (a-*this).cross(b-*this); }
	T dist2() const { return x*x + y*y; }
	ld dist() const { return sqrtl((ld)dist2()); }
	// angle to x-axis in interval [-pi, pi]
	ld angle() const { return atan2(y, x); }
	P unit() const { return *this/dist(); } // makes dist()=1
	P perp() const { return P(-y, x); } // rotates +90 degrees
	P normal() const { return perp().unit(); }
	// returns point rotated 'a' radians ccw around the origin
	P rotate(ld a) const {
		return P(x*cos(a)-y*sin(a),x*sin(a)+y*cos(a)); }
	friend ostream& operator<<(ostream& os, P p) {
		return os << "(" << p.x << "," << p.y << ")"; }
};
template<class P>
vector<P> circleLine(P c, ld r, P a, P b) {
	P ab = b - a, p = a + ab * (c-a).dot(ab) / ab.dist2();
	ld s = a.cross(b, c), h2 = r*r - s*s / ab.dist2();
	if (h2 < 0) return {};
	if (h2 == 0) return {p};
	P h = ab.unit() * sqrtl(h2);
	return {p - h, p + h};
}

ld gss(ld a, ld b, function<ld(ld)> f) {
	ld r = (sqrtl(5)-1)/2, eps = 1e-8;
	ld x1 = b - r*(b-a), x2 = a + r*(b-a);
	ld f1 = f(x1), f2 = f(x2);
	while (b-a > eps) {
		if (f1 < f2) { //change to > to find maximum
			b = x2; x2 = x1; f2 = f1;
			x1 = b - r*(b-a); f1 = f(x1);
		} else {
			a = x1; x1 = x2; f1 = f2;
			x2 = a + r*(b-a); f2 = f(x2);
		}
	}
	return a;
}

ld s;

int n;
vector<Point<ld>> p;
int main() {
	cin >> s;
	s -= eps;
	cin >> n;
	p.resize(n);
	for (auto &[i, j] : p) {
		int x, y ; cin >> x >> y;
		i = x;j = y;
	}
	for (int i = n-1; i >= 0; i--) {
		p[i] = p[i] - p[0];
	}


	Point<ld> me = p[0], partner;
	bool started = false;
	int i = 0, j = -1;
	const ld inf = 1e18;
	ld ans = inf;
	bool bum = 0;
	ld trav = 0;
	while (i < n-1) {
		if (started) {
			ans = min((me-partner).dist(), ans);
		}
		int stepType = -1;

		ld nextT = inf;
		if (i < n-1) {
			ld o = (me-p[i+1]).dist2();
			if (o < nextT) {
				stepType = 0;
				nextT = o;
			}
		}

		if (started) {
			ld o = (partner - p[j+1]).dist2();
			if (o < nextT) {
				nextT = o;
				stepType = 1;
			}
			auto partnerDir = (p[j+1]-p[j]).unit();
			auto dir = (p[i+1]-p[i]).unit();

			if (!bum) {
				function<ld(ld)> dis = [&](ld t) ->ld {
					return (me + dir*t - partner - partnerDir*t).dist2();
				};
				// weird shit
				o = gss(-1, min((p[j+1]-p[j]).dist(), (p[i+1]-p[i]).dist()), dis);
				if (o*o < nextT && o > 0) {
					nextT = o*o;
					stepType = 3;
				}
			}
		}
		else {
			ld dis = s-trav;
			ld o = (p[i+1]-p[i]).dist();
			if (dis < o && dis > 0) {
				o = dis*dis;
				if (o < nextT) {
					nextT = o;
					stepType = 2;
				}
			}
		}
		nextT = sqrtl(nextT);
		if (started) {
			auto partnerDir = (p[j+1]-p[j]).unit();
			partner = partner+partnerDir*nextT;
		}
		auto dir = (p[i+1]-p[i]).unit();
		trav += nextT;
		me = me+dir*nextT;
		if (stepType == 0) {
			i++;
			me = p[i];
		}
		else if (stepType == 1) {
			j++;
			partner = p[j];
		}
		else if (stepType == 2) {
			j = 0;
			started = true;
			partner = p[0];
		}
		if (stepType == 3) {
			bum = true;
		}
		else {
			bum = false;
		}
	}

	cout << setprecision(20) << fixed << ans << endl;

}