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

//#define int long long
#define DBG 1
#define dump(o) if(DBG){cerr<<#o<<" "<<(o)<<" ";}
#define dumpl(o) if(DBG){cerr<<#o<<" "<<(o)<<endl;}
#define dumpc(o) if(DBG){cerr<<#o; for(auto &e:(o))cerr<<" "<<e;cerr<<endl;}
#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define all(c) begin(c),end(c)
const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = (int)(1e9 + 7);

/*

Todo:
Line??¨Segment?????????????????????

*/

const double EPS = 1e-10;
#define equals(a,b) (fabs((a)-(b)) < EPS)
#define next(P,i) P[(i+1)%P.size()]
#define prev(P,i) P[(i+P.size()-1)%P.size()]

//0?¬?
class Point {
public:
	double x, y;
	Point() {}
	Point(double x, double y) :x(x), y(y) {}

	Point operator+(Point p) { return Point(x + p.x, y + p.y); }
	Point operator-(Point p) { return Point(x - p.x, y - p.y); }
	Point operator*(double a) { return Point(a * x, a * y); }
	Point operator/(double a) { return Point(x / a, y / a); }
	bool operator<(const Point &p)const {
		//return y != p.y ? y < p.y : x < p.x; // y?????? -> x??????
		return x != p.x ? x < p.x : y < p.y; // x?????? -> y??????
	}
	bool operator==(const Point &p)const { return equals(x, p.x) && equals(y, p.y); }

	double abs() { return sqrt(norm()); }
	double norm() { return x*x + y*y; }
};
inline ostream &operator << (ostream &os, const Point &p) { os << p.x << " " << p.y; return os; }
inline istream &operator >> (istream &is, Point &p) { double x, y; is >> x >> y; p = Point(x, y); return is; }

//1?¬?
class Vector :public Point {
public:
	using Point::Point;
	Vector(const Point &P) { x = P.x; y = P.y; }
	Vector rotate(double rad) { return Vector(x*cos(rad) - y*sin(rad), x*sin(rad) + y*cos(rad)); }
};

class Line {
public:
	Point p1, p2;
	Line() {}
	Line(Point p1, Point p2) :p1(p1), p2(p2) {}
};
class Segment :public Line {
public:
	using Line::Line;
	Segment(const Line &L) { p1 = L.p1; p2 = L.p2; }
	Vector vec() { return p2 - p1; }
};


//2?¬?
class Circle {
public:
	Point c; //center
	double r; //radius
	Circle() {}
	Circle(Point c, double r) :c(c), r(r) {}
};
using Polygon = vector<Point>;

//?????? dot product
double dot(Vector a, Vector b) { return a.x*b.x + a.y*b.y; }
//?????? cross product ?????§???????????£????????????
double cross(Vector a, Vector b) { return a.x*b.y - a.y*b.x; }

//????????¢??? radian ??? ??? degree
double rad(double deg) { return acos(-1)*deg / 180; }
//????§? argument
double arg(Vector p) { return atan2(p.y, p.x); }
//?\???¢??? polar form
Vector polar(double r, double a) { return Point(cos(a)*r, sin(a)*r); }

bool inrange(Point p, double x1, double y1, double x2, double y2) {
	return x1 <= p.x&&p.x <= x2&&y1 <= p.y&&p.y <= y2;
}

//??´?????????
bool is_orthogonal(Vector a, Vector b) { return equals(dot(a, b), 0.0); }
bool is_orthogonal(Point a1, Point a2, Point b1, Point b2) { return is_orthogonal(a1 - a2, b1 - b2); }
bool is_orthogonal(Segment s1, Segment s2) { return equals(dot(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0); }

//????????????
bool is_parallel(Vector a, Vector b) { return equals(cross(a, b), 0.0); }
bool is_parallel(Point a1, Point a2, Point b1, Point b2) { return is_parallel(a1 - a2, b1 - b2); }
bool is_parallel(Segment s1, Segment s2) { return equals(cross(s1.p2 - s1.p1, s2.p2 - s2.p1), 0.0); }

//?°???±
Point project(Segment s, Point p) {
	Vector base = s.p2 - s.p1;
	double r = dot(p - s.p1, base) / base.norm();
	return s.p1 + base*r;
}
//????°?
Point reflect(Segment s, Point p) { return p + (project(s, p) - p)*2.0; }

//??????(p0,p1)????????????p2???????????¢???
enum { ONLINE_FRONT = -2, CLOCKWISE, ON_SEGMENT, COUNTER_CLOCKWISE, ONLINE_BACK };
int ccw(Point p0, Point p1, Point p2) {
	Vector a = p1 - p0, b = p2 - p0;
	if (cross(a, b) > EPS)return COUNTER_CLOCKWISE;
	if (cross(a, b) < -EPS)return CLOCKWISE;
	if (dot(a, b) < -EPS)return ONLINE_BACK; //p2 p0 p1
	if (a.norm() < b.norm())return ONLINE_FRONT; //p0 p1 p2
	return ON_SEGMENT;
}
int ccw(Vector a, Vector b) {
	if (cross(a, b) > EPS)return COUNTER_CLOCKWISE;
	if (cross(a, b) < -EPS)return CLOCKWISE;
	if (dot(a, b) < -EPS)return ONLINE_BACK; //p2 p0 p1
	if (a.norm() < b.norm())return ONLINE_FRONT; //p0 p1 p2
	return ON_SEGMENT;
}

//??´?????¨??´??????????????????
bool intersect(Point p1, Point p2, Point p3, Point p4) {
	return (ccw(p1, p2, p3)*ccw(p1, p2, p4) <= 0 &&
		ccw(p3, p4, p1)*ccw(p3, p4, p2) <= 0);
}
bool intersect(Segment s1, Segment s2) { return intersect(s1.p1, s1.p2, s2.p1, s2.p2); }
//(?????????????¶????)

//2??????????????¢
double get_distance(Point a, Point b) { return (a - b).abs(); }
//??´?????¨???????????¢
double get_distance(Line l, Point p) { return abs(cross(l.p2 - l.p1, p - l.p1) / (l.p2 - l.p1).abs()); }
//????????¨???????????¢
double get_distance(Segment s, Point p) {
	if (dot(s.p2 - s.p1, p - s.p1) < 0.0)return (p - s.p1).abs();
	if (dot(s.p1 - s.p2, p - s.p2) < 0.0)return (p - s.p2).abs();
	return get_distance(Line(s), p);
}
//????????¨??????????????¢
double get_distance(Segment s1, Segment s2) {
	if (intersect(s1, s2))return 0.0;
	return	min(
		min(get_distance(s1, s2.p1), get_distance(s1, s2.p2)),
		min(get_distance(s2, s1.p1), get_distance(s2, s1.p2))
	);
}

//?????¨??´??????????????????
bool intersect(Circle c, Line l) { return get_distance(l, c.c) <= c.r + EPS; }
//?????¨?????????????????? ??±?????\????????°
int intersect(Circle c1, Circle c2) {
	double d = get_distance(c1.c, c2.c);
	if (d > c1.r + c2.r)return 4;
	if (d == c1.r + c2.r)return 3;
	if (d + c1.r == c2.r || d + c2.r == c1.r)return 1;
	if (d + c1.r < c2.r || d + c2.r < c1.r)return 0;
	return 2;
}

//????????¨???????????????
Point get_cross_point(Segment s1, Segment s2) {
	assert(intersect(s1, s2));
	Vector base = s2.p2 - s2.p1;
	double a1 = abs(cross(base, s1.p1 - s2.p1)); //area1
	double a2 = abs(cross(base, s1.p2 - s2.p1)); //area2
	double t = a1 / (a1 + a2);
	return s1.p1 + (s1.p2 - s1.p1)*t;
}
//??´?????¨??´????????????
//Point get_cross_point(Line l1, Line l2) {}

//?????¨??´????????????
pair<Point, Point> get_cross_points(Circle c, Line l) {
	assert(intersect(c, l));
	Vector pr = project(l, c.c);
	Vector e = (l.p2 - l.p1) / (l.p2 - l.p1).abs();
	double base = sqrt(c.r*c.r - (pr - c.c).norm());
	return make_pair(pr + e*base, pr - e*base);
}
//?????¨????????????
pair<Point, Point> get_cross_points(Circle c1, Circle c2) {
	int m = intersect(c1, c2);
	assert(m != 4 && m != 0);
	double d = (c1.c - c2.c).abs();
	double a = acos((c1.r*c1.r + d*d - c2.r*c2.r) / (2 * c1.r*d));
	double t = arg(c2.c - c1.c);
	return make_pair(c1.c + polar(c1.r, t + a), c1.c + polar(c1.r, t - a));
}

//????????????
enum { OUT = 0, ON, IN };
int contains(Polygon g, Point p) {
	int n = g.size();
	bool x = false;
	for (int i = 0; i < n; i++) {
		Point a = g[i] - p, b = g[(i + 1) % n] - p;
		if (abs(cross(a, b)) < EPS&&dot(a, b) < EPS)return ON;
		if (a.y > b.y)swap(a, b);
		if (a.y < EPS&&EPS<b.y&&cross(a, b)>EPS)x = !x;
	}
	return (x ? IN : OUT);
}

int contains(Circle c, Point p) {
	double d = get_distance(c.c, p);
	if (equals(d, c.r))return ON;
	if (d < c.r)return IN;
	return OUT;
}

//????§???¢?????¢???
double area(Polygon g) {
	double a = 0;
	for (size_t i = 0; i < g.size(); i++)
		a += cross(g[i], g[(i + 1) % g.size()]);
	return a / 2.0;
}

//?????§????????????????¨??????????
bool is_convex(Polygon g) {
	for (size_t i = 0; i < g.size(); i++)
		if (ccw(g[i], g[(i + 1) % g.size()], g[(i + 2) % g.size()]) == CLOCKWISE)
			return false;
	return true;
}

//??????
//Graham scan https://en.wikipedia.org/wiki/Graham_scan
//???????????????????????????
Polygon convex_hull(Polygon P) {
	sort(P.begin(), P.end());
	Polygon up;
	for (Point &p : P) {
		while (up.size() > 1 && ccw(up[up.size() - 2], up[up.size() - 1], p) != CLOCKWISE)up.pop_back();
		up.emplace_back(p);
	}
	Polygon down;
	for (Point &p : P) {
		while (down.size() > 1 && ccw(down[down.size() - 2], down[down.size() - 1], p) != COUNTER_CLOCKWISE)down.pop_back();
		down.emplace_back(p);
	}
	reverse(up.begin(), up.end()); // ???????¨??????????
	down.insert(down.end(), up.begin() + 1, up.end() - 1);
	return down;
}

//??????
//Graham scan https://en.wikipedia.org/wiki/Graham_scan
//?????????????????????
Polygon convex_hull_with_points_online(Polygon P) {
	sort(P.begin(), P.end());
	Polygon up;
	for (Point &p : P) {
		int _ccw;
		while (up.size() > 1 && (_ccw = ccw(up[up.size() - 2], up[up.size() - 1], p)) != CLOCKWISE &&_ccw != ONLINE_FRONT)
			up.pop_back();
		up.emplace_back(p);
	}
	Polygon down;
	for (Point &p : P) {
		int _ccw;
		while (down.size() > 1 && (_ccw = ccw(down[down.size() - 2], down[down.size() - 1], p)) != COUNTER_CLOCKWISE && _ccw != ONLINE_FRONT)
			down.pop_back();
		down.emplace_back(p);
	}
	reverse(up.begin(), up.end()); // ???????¨??????????
	down.insert(down.end(), up.begin() + 1, up.end() - 1);
	return down;
}

//???????§???¢??????????????????????????¢
//calipers https://en.wikipedia.org/wiki/Rotating_calipers
double diameter(Polygon P) {
	P = convex_hull(P);
	auto mima = minmax_element(P.begin(), P.end());
	int I = mima.first - P.begin();
	int J = mima.second - P.begin();
	double maxd = get_distance(P[I], P[J]);

	int maxi, maxj, i, j;
	i = maxi = I;
	j = maxj = J;
	do {
		if (ccw(next(P, i) - P[i], next(P, j) - P[j]) == COUNTER_CLOCKWISE)
			j = (j + 1) % P.size();
		else
			i = (i + 1) % P.size();
		if (maxd < get_distance(P[i], P[j])) {
			maxd = get_distance(P[i], P[j]);
			maxi = i, maxj = j;
		}
	} while (!(i == I&&j == J));
	return maxd;
}

#define idx(i) (i+25)
template<class T> bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; }
template<class T> bool chmin(T &a, const T &b) { if (a > b) { a = b; return true; } return false; }
signed main() {
	cout << fixed << setprecision(6);
	for (int r, n; cin >> r >> n&&r;) {
		int Hl[50] = {};
		int Hr[50] = {};
		rep(i, 0, n) {
			int xl, xr, h; cin >> xl >> xr >> h;
			rep(j, xl, xr) {
				chmax(Hl[idx(j)], h);
			}
			rep(j, xl + 1, xr + 1) {
				chmax(Hr[idx(j)], h);
			}
		}
		double miny = INF;
		Line L(Point(0, 0), Point(0, 1));
		rep(x, -20, 20 + 1) {
			Circle C(Point(x, min(Hl[idx(x)], Hr[idx(x)])), r);
			if (!intersect(C, L))continue;
			auto cp = get_cross_points(C, L);
			if (cp.first == cp.second)continue;
			chmin(miny, cp.first.y);
			chmin(miny, cp.second.y);
		}
		cout << max(-(double)r, miny) + r << endl;
	}
	return 0;
}

Measured memory_bytes: 3204