#include <bits/stdc++.h>
#define syosu(x) fixed<<setprecision(x)
using namespace std;
typedef long long ll;
typedef unsigned int uint;
typedef unsigned long long ull;
typedef pair<int,int> P;
typedef pair<double,double> pdd;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<double> vd;
typedef vector<vd> vvd;
typedef vector<ll> vl;
typedef vector<vl> vvl;
typedef vector<string> vs;
typedef vector<P> vp;
typedef vector<vp> vvp;
typedef vector<pll> vpll;
typedef pair<int,P> pip;
typedef vector<pip> vip;
const int inf=1<<29;
const ll INF=1ll<<60;
const double pi=acos(-1);
const double eps=1e-9;
const ll mod=1e9+7;
const int dx[4]={-1,0,1,0},dy[4]={0,-1,0,1};

const int M=20;

int main(){
	ios::sync_with_stdio(0);
	cin.tie(0);
	while(1){
		int r,n;
		cin>>r>>n;
		if(r==0) break;
		vi a(2*M);
		for(int i=0;i<n;i++){
			int l,r,h;
			cin>>l>>r>>h;
			l+=M,r+=M;
			for(int j=l;j<r;j++) a[j]=max(a[j],h);
		}
		double res=inf;
		for(int i=0;i<2*M;i++){
			int d=(i<M?M-i-1:i-M);
			if(r>d){
				res=min(res,r+a[i]-sqrt(r*r-d*d));
			}
		}
		cout<<syosu(9)<<res<<endl;
	}
}
