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

using db = double;

constexpr db eps = 1e-6;

int cmp(db a, db b) {
	if (a - b > eps) {
		return 1;
	}
	if (a - b < -eps) {
		return -1;
	}
	return 0;
}

struct Point {
	db x, y;

	Point operator+(const Point& a) {
		return {x + a.x, y + a.y};
	}
	Point operator-(const Point& a) {
		return {x - a.x, y - a.y};
	}
	Point operator*(const db& a) {
		return {x * a, y * a};
	}
	Point operator/(const db& a) {
		return {x / a, y / a};
	}

	db len2() {
		return x * x + y * y;
	}
	db len() {
		return sqrt(len2());
	}
	Point unit() {
		return (*this) / len();
	}
};

db dis(Point a, Point b) {
	return (b - a).len();
}

int main() {
	ios::sync_with_stdio(false);
	cin.tie(nullptr);

	cout << fixed << setprecision(10);

	db s;
	int n;
	cin >> s >> n;

	vector<Point> A(n);
	for (auto &[x, y] : A) {
		cin >> x >> y;
	}

	vector<db> sum(n);
	vector<db> tim;
	for (int i = 0; i < n - 1; i++) {
		sum[i + 1] = sum[i] + dis(A[i], A[i + 1]);
	}

	for (int i = 0; i < n; i++) {
		if (cmp(sum[i] + s, sum[n - 1]) <= 0) {
			tim.push_back(sum[i]);
		} 
		if (cmp(sum[i], s) >= 0) {
			tim.push_back(sum[i] - s);
		}
	}
	sort(tim.begin(), tim.end());

	Point dir1, dir2;
	int i1 = 0, i2 = 0;
	db ans = 1e18;
	for (int i = 0; i < tim.size() - 1; i++) {
		db t1 = tim[i], t2 = tim[i + 1];
		if (cmp(t1, t2) == 0) {
            continue;
        }
        int l = -1, r = n;
        while (l + 1 != r) {
            int m = (l + r) / 2;
            if (cmp(sum[m], t1) <= 0) {
                l = m;
            } else {
                r = m;
            }
        }
        i1 = l;

        l = -1, r = n;
        while (l + 1 != r) {
            int m = (l + r) / 2;
            if (cmp(sum[m], t1 + s) <= 0) {
                l = m;
            } else {
                r = m;
            }
        }
        i2 = l;
        
		// while (i1 + 1 < n && cmp(sum[i1 + 1], t1) <= 0) {
		// 	i1++;
		// }
		// while (i2 + 1 < n && cmp(sum[i2 + 1], t1 + s) <= 0) {
		// 	i2++;
		// }

        Point v1 = (A[i1 + 1] - A[i1]).unit();
        Point v2 = (A[i2 + 1] - A[i2]).unit();


		Point p1 = A[i1] + v1 * (t1 - sum[i1]);
		Point p2 = A[i2] + v2 * (t1 + s - sum[i2]);

        auto calc = [&](db t) {
			return dis(p1 + v1 * t, p2 + v2 * t);
		};
		
		db lo = 0, hi = t2 - t1;
		while (hi - lo > eps) {
			// cerr << lo << " " << hi << "\n";
			db lm = (2 * lo + hi) / 3;
			db rm = (lo + 2 * hi) / 3;
			if (calc(lm) > calc(rm)) {
				lo = lm;
			} else {
				hi = rm;
			}
		}

		// dir1 = (A[i1 + 1] - A[i1]).unit();
	 	// dir2 = (A[i2 + 1] - A[i2]).unit();
		
		// auto calc = [&](db t) {
		// 	Point a = A[i1] + dir1 * (t - sum[i1]); 
		// 	Point b = A[i2] + dir2 * (t + s - sum[i2]);
		// 	return dis(a, b);
		// };
		
		// while (t2 - t1 > eps) {
		// 	db lm = (2 * t1 + t2) / 3;
		// 	db rm = (t1 + 2 * t2) / 3;
		// 	if (calc(lm) > calc(rm)) {
		// 		t1 = lm;
		// 	} else {
		// 		t2 = rm;
		// 	}
		// }

		ans = min(ans, calc(lo));
	}

	cout << ans << "\n";
	return 0;
}