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

#define fs first
#define sc second

template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }


// std::vector Declaration
template<typename T>
vector<T> make_v(size_t a) { return vector<T>(a); }
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts) {
    return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}

// std::vector Initialization
template<typename T>
void fill_all(T& arr, const T& v) { arr = v; }
template<typename T, typename U>
void fill_all(T& arr, const U& v) { for (auto& i : arr) fill_all(i, v); }

// std::vector Debug
template<typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
    os << "[";
    bool a = 1;
    for (auto e : v ) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "]";
    return os;
}

// std::pair Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const pair<T, U>& p) {
    os << "(" << p.first << " " << p.second << ")";
    return os;
}

// std::set Debug
template<typename T>
ostream& operator<<(ostream& os, const set<T>& st) {
    os << "{";
    bool a = 1;
    for (auto e : st) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "}";
    return os;
}

// std::multiset Debug
template<typename T>
ostream& operator<<(ostream& os, const multiset<T>& st) {
    os << "{";
    bool a = 1;
    for (auto e : st) {
        os << (a ? "" : " ");
        os << e;
        a = 0;
    }
    os << "}";
    return os;
}

// std::map Debug
template<typename T, typename U>
ostream& operator<<(ostream& os, const map<T, U>& mp) {
    os << "{";
    bool a = 1;
    for (auto e : mp) {
        os << (a ? "" : " ");
        os << e.first << ":" << e.second;
        a = 0;
    }
    os << "}";
    return os;
}

// std::tuple Debug
template<int N, class Tuple>
void out(ostream& os, const Tuple& t){}
template<int N, class Tuple, class H, class ...Ts>
void out(ostream& os, const Tuple& t) {
    if (N) os << " ";
    os << get<N>(t);
    out<N+1,Tuple,Ts...>(os, t);
}
template<class ...Ts>
ostream& operator<<(ostream& os, const tuple<Ts...>& t) {
    os << "(";
    out<0,tuple<Ts...>,Ts...>(os, t);
    os << ")";
    return os;
}

// Debug
#define DUMP(x) cerr<<#x<<" = "<<(x)<<endl


struct edge { int to, cost; };
ostream& operator<<(ostream& os, const edge& e) {
    os << "(" << e.to << ", " << e.cost << ")";
    return os;
}

const LL LINF = 1LL<<60;
const int IINF = 1<<30;
const LL MOD = 1e9+7;

int main()
{
    vector<int> rs, ns;
    vector<vector<int>> xls, xrs, ys;
    while (true) {
        int r, n; cin >> r >> n;
        if (r == 0 && n == 0) {
            break;
        }
        vector<int> xl(n), xr(n), y(n);
        for (int i = 0; i < n; ++i) {
            cin >> xl[i] >> xr[i] >> y[i];
        }
        rs.push_back(r);
        ns.push_back(n);
        xls.push_back(xl);
        xrs.push_back(xr);
        ys.push_back(y);
    }

    for (int t = 0; t < ns.size(); ++t) {
        int r = rs[t], n = ns[t];
        auto xl = xls[t], xr = xrs[t], y = ys[t];

        auto s = make_v<int>(20+20, 20+1);
        for (int i = 0; i < n; ++i) {
            for (int X = xl[i]; X < xr[i]; ++X) {
                for (int Y = 0; Y < y[i]; ++Y) {
                    s[X+20][Y] = 1;
                }
            }
        }

        double ans = 1e9;
        for (int i = 0; i < 40; ++i) {
            for (int j = 0; j <= 20; ++j) {
                if (s[i][j] == 0) {
                    int X = i-20, Y = j;
                    if (X < 0) {
                        X += 1;
                    }
                    if (r*r - X*X <= 0) {
                        continue;
                    }
                    double h = sqrt(r*r - X*X);
                    chmin(ans, Y-h);
                }
            }
        }
        printf("%.4lf\n", max(ans+r, 0.));
    }

    return 0;
}



Measured memory_bytes: 3232