import java.util.*;
public class Main {
  private static final int LIM = 20;
  public static void main(String[] args) {
    final Scanner sc = new Scanner(System.in);
    while(sc.hasNext()) {
      final int r = sc.nextInt();
      final int n = sc.nextInt();
      if(r == 0 && n == 0)
        return;
      final int[] xl = new int[n];
      final int[] xr = new int[n];
      final int[] h  = new int[n];
      for(int i = 0; i < n; i++) {
        xl[i] = sc.nextInt();
        xr[i] = sc.nextInt();
        h[i]  = sc.nextInt();
      }
      final int[] hmax = new int[2 * LIM];
      for(int i = 0; i < n; i++)
        for(int j = xl[i]; j < xr[i]; j++)
          hmax[j+LIM] = Math.max(hmax[j+LIM], h[i]);
      for(int i = -LIM; i < LIM; i++)
          if(hmax[i+LIM] == Integer.MAX_VALUE)
            hmax[i+LIM] = 0;
      double ans = Double.POSITIVE_INFINITY;
      for(int i = -r; i < r; i++) {
        final int x = i < 0 ? ~i : i;
        ans = Math.min(ans, hmax[i+LIM] + r - Math.sqrt(r * r - x * x));
      }
      System.out.println(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