#include <bits/stdc++.h>
                            #include<iostream>
                            #include<cstdio>
                            #include<vector>
                            #include<queue>
                            #include<map>
                            #include<cstring>
                            #include<string>
                            #include <math.h>
                            #include<algorithm>
                        //    #include <boost/multiprecision/cpp_int.hpp>
                            #include<functional>
                 //    #define int long long
                            #define inf  1000000007
                            #define pa pair<int,int>
                            #define ll long long
                            #define pal pair<double,pa>
                            #define ppa pair<pa,int>
                            #define ppap pair<int,pa>
                            #define ssa pair<string,int>
                            #define  mp make_pair
                            #define  pb push_back
                            #define EPS (1e-10)
                            #define equals(a,b) (fabs((a)-(b))<EPS)
                     
                            using namespace std;
                     //priority_queue<int, vector<int>, greater<int> > que;
                            class Point{
                            	public:
                            	double x,y;
                            	Point(double x=0,double y=0):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(x*a,y*a);}
                            	Point operator / (double a) {return Point(x/a,y/a);}
                            	double absv() {return sqrt(norm());}
                            	double norm() {return x*x+y*y;}
                            	bool operator < (const Point &p) const{
                            		return x != p.x ? x<p.x: y<p.y;
                            	}
                            	bool operator == (const Point &p) const{
                            		return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
                            	}
                            };
                            typedef Point Vector;
                     
                            struct Segment{
                            Point p1,p2;
                            };
                     
                        double hen(Vector a){
                        if(fabs(a.x)<EPS && a.y>0) return acos(0);
                        else if(fabs(a.x)<EPS && a.y<0) return 3*acos(0);
                        else if(fabs(a.y)<EPS && a.x<0) return 2*acos(0);
                        else if(fabs(a.y)<EPS && a.x>0) return 0.0;
                        else if(a.y>0) return acos(a.x/a.absv());
                        else return 2*acos(0)+acos(-a.x/a.absv());
                     
                        }
                     
                string itos( int i ) {
                ostringstream s ;
                s << i ;
                return s.str() ;
                }
                 
                int gcd(int v,int b){
                	if(v>b) return gcd(b,v);
                	if(v==b) return b;
                	if(b%v==0) return v;
                	return gcd(v,b%v);
                }
                            double dot(Vector a,Vector b){
                            	return a.x*b.x+a.y*b.y;
                            }
                            double cross(Vector a,Vector b){
                            	return a.x*b.y-a.y*b.x;
                            }
                        
                double distans(double x1,double y1,double x2,double y2){
                	double rr=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
                	return sqrt(rr);
                	
                }
                /*}
int pr[100010];
//int inv[100010];
 
int beki(int wa,int rr){
	if(rr==0) return 1ll;
	if(rr==1) return wa;
	if(rr%2==1) return (beki(wa,rr-1)*wa)%inf;
	int zx=beki(wa,rr/2);
	return (zx*zx)%inf;
}
  
void gya(){
	pr[0]=1;
	for(int i=1;i<100010;i++){
		pr[i]=(pr[i-1]*i)%inf;
	}
	for(int i=0;i<100010;i++) inv[i]=beki(pr[i],inf-2);
	
}

*/

                         //----------------kokomade tenpure------------


string s[50],t[50];
signed main(){
	int n,m,r;
	/*
	double d;
	cin>>d;
	
	double ans=0;
	for(int i=0;i<=10;i++){
		if(i>d) break;
		double ii=i+0.0;
		ans=max(ans,sqrt(d*d-ii*ii));
	}
	printf("%.10lf\n",ans);
	*/
	
	while(1){
	cin>>r>>n;
		//int sumi[200]={0};
		if(n==0&&r==0) return 0;
		int a[100]={0};
		for(int i=0;i<n;i++){
			int x2,x1,h;
			cin>>x1>>x2>>h;
			for(int i=x1+50+1;i<=x2+50;i++) a[i]=max(a[i],h);
		}
		int aa[100]={0};
//		for(int i=50-r;i<=50+r;i++) cout<<aa[i]<<endl;
		for(int i=50-r-2;i<=r+50+2;i++) aa[i]=min(a[i],a[i+1]);
	//		for(int i=50-r;i<=50+r;i++) cout<<i-50<<" "<<aa[i]<<endl;
		double ans=1000000000;
		for(int i=50-r+1;i<=50+r-1;i++){
			int d=i-50;
			double w=(r+0.0)-sqrt((r+0.0)*(r+0.0)-(d+0.0)*(d+0.0));
			ans=min(ans,aa[i]+w)	;
		}
		printf("%.10lf\n",ans);
		
		
	}
	
	
	return 0;
}

Measured memory_bytes: 3128