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

#define eb emplace_back
#define all(s) (s).begin(), (s).end()
#define rep(i, a, b) for (int i = (a); i <= (b); ++i)
#define per(i, a, b) for (int i = (a); i >= (b); --i)

#define N 1000007

struct P {
    double x, y;
    P operator + (const P &p) const {return {x + p.x, y + p.y};}
    P operator - (const P &p) const {return {x - p.x, y - p.y};}
    P operator * (const double &d) const {return {x * d, y * d};}
    P operator / (const double &d) const {return {x / d, y / d};}
} p[N], u[N];

double abs(const P &p) {return sqrt(p.x * p.x + p.y * p.y);}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    double s; cin >> s;
    int n; cin >> n;
    rep(i, 1, n) {
        cin >> p[i].x >> p[i].y;
        u[i] = (p[i] - p[i - 1]) / abs(p[i] - p[i - 1]);
    }
    double ans = s;
    int tara = 2, tarb = 2;
    P posa = p[1], posb = p[1];
    for (double d = 0; tarb <= n && d < s; ) {
        double _d = abs(posb - p[tarb]);
        if (d + _d >= s) {
            posb = posb + u[tarb] * (s - d);
            break;
        } else {posb = p[tarb++]; d += _d;}
    }
    ans = min(ans, abs(posa - posb));
    auto calc = [&](const P &p1, const P &p2, const P &q1, const P &q2) {
        double l = 0, r = 1;
        auto getd = [&](double ra) {
            P pp = p1 * ra + p2 * (1 - ra);
            P qq = q1 * ra + q2 * (1 - ra);
            return abs(pp - qq);
        };
        rep(i, 1, 30) {
            double lmid = l + (r - l) / 3;
            double rmid = r - (r - l) / 3;
            double ansl = getd(lmid), ansr = getd(rmid);
            ans = min({ans, ansl, ansr});
            ansl < ansr ? r = rmid : l = lmid;
        }
    };
    while (tarb <= n) {
        if (tara == tarb) {
            posa = p[tara] - u[tara] * s;
            posb = p[tarb++];
        }
        if (tarb > n) break;
        double d1 = abs(posa - p[tara]);
        double d2 = abs(posb - p[tarb]);
        if (d1 < d2) {
            P _posb = posb + u[tarb] * d1;
            calc(posa, p[tara], posb, _posb);
            posa = p[tara++]; posb = _posb;
        } else {
            P _posa = posa + u[tara] * d2;
            calc(posa, _posa, posb, p[tarb]);
            posa = _posa; posb = p[tarb++];
        }
    }
    printf("%.10lf\n", ans);
    return 0;
}