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

#define int long long

using db = double;
const db eps = 1e-9;

int sgn(db k) {
    if (k > eps) {
        return 1;
    }
    if (k < -eps) {
        return -1;
    }
    return 0;
}
int cmp(db a, db b) {
    return sgn(a - b);
}
struct point {
    db x, y;
    point operator + (const point &k) {
        return {x + k.x, y + k.y};
    }
    point operator - (const point &k) {
        return {x - k.x, y - k.y};
    }
    point operator * (const db &k) {
        return {x * k, y * k};
    }
    point operator / (const db &k) {
        return {x / k, y / k};
    }
    
    friend istream &operator >> (istream &is, point &p) {
        return is >> p.x >> p.y;
    }
    friend ostream &operator << (ostream &os, point &p) {
        return os << p.x << " " << p.y;
    }

    db len2() {
        return x * x + y * y;
    }
    db len() {
        return sqrt(len2());
    }
    point unit() {
        return (*this) / len();
    }
};
db dis(point p1, point p2) {
    return sqrt((p1 - p2).len2());
}
signed main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(10);
    db d;
    cin >> d;
    int n;
    cin >> n;
    vector<db> s(n + 1);
    vector<point> p(n + 1);
    for (int i = 1; i <= n; i++) {
        cin >> p[i];
    }
    for (int i = 2; i <= n; i++) {
        s[i] = s[i - 1] + dis(p[i - 1], p[i]);
    }
    vector<db> tim;
    for (int i = 1; i <= n; i++) {
        tim.push_back(s[i]);
        tim.push_back(s[i] + d);
    }
    auto find = [&] (db t) {
        int l = 0, r = n;
        while (l + 1 != r) {
            int m = (l + r) / 2;
            if (cmp(s[m], t) <= 0) {
                l = m;
            } else {
                r = m;
            }
        }
        point v = (p[l + 1] - p[l]).unit();
        point ret = p[l] + v * (t - s[l]);
        return make_pair(ret, v);
    };
    sort(tim.begin(), tim.end());
    db ans = 1e18;
    for (int i = 1; i < tim.size(); i++) {
        db t1 = tim[i - 1], t2 = tim[i];
        if (cmp(t1, t2) == 0 || cmp(t1, s[n]) == 1 || cmp(t2, s[n]) == 1 || cmp(t1, d) == -1 || cmp(t2, d) == -1) {
            continue;
        }
        // cerr << t1 << " " << t2 << "\n";
        auto [p1, v1] = find(t1 - d);
        auto [p2, v2] = find(t1);
        db l = 0, r = t2 - t1;
        auto calc = [&] (db t) {
            point a = p1 + v1 * t;
            point b = p2 + v2 * t;
            return dis(a, b);
        };
        while (r - l > 1e-9) {
            db lm = (2 * l + r) / 3;
            db rm = (2 * r + l) / 3;
            if (calc(lm) > calc(rm)) {
                l = lm;
            } else {
                r = rm;
            }
        }
        ans = min(ans, calc(l));
        ans = min(ans, calc(r));
    }
    cout << ans << "\n";
    return 0;
}