#include <cstdio>
#include <iostream>
#include <complex>
#include <vector>
#include <utility>
#include <algorithm>
#include <cassert>
#include <queue>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <map>
using namespace std;
 
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
 
int R, N;
 
int main() {
  for (;;) {
    cin >> R >> N;
    if (R == 0 && N == 0) return 0;
 
    map<int, int> hmax;
 
    rep (i, N) {
      int x1, x2, h;
      cin >> x1 >> x2 >> h;
      for (int x = x1; x < x2; ++x) hmax[x] = max(hmax[x], h);
    }
 
    double ans = 1E30;
    for (int x0 = -R; x0 < R; ++x0) {
      int h = hmax[x0];
      for (int x = x0; x <= x0 + 1; ++x) {
        ans = min(ans, h - sqrt(R * R - x * x) + R);
      }
    }
    printf("%.10f\n", ans);
  }
}
 

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2 3
-2 -1 3
0 1 3
2 3 3
2 2
-2 0 4
0 2 3
2 6
-3 3 1
-2 3 2
-1 3 3
0 3 4
1 3 5
2 3 6
2 6
-3 3 1
-3 2 2
-3 1 3
-3 0 4
-3 -1 5
-3 -2 6
0 0