You are given a set of circles \textbf{C} of a variety of radii (radiuses) placed at a variety of positions, possibly overlapping one another. Given a circle with radius \textbf{r}, that circle may be placed so that it encircles all of the circles in the set \textbf{C} if \textbf{r} is large enough. There may be more than one possible position of the circle of radius \textbf{r} to encircle all the member circles of \textbf{C}. We de ne the region \textbf{U} as the union of the areas of encircling circles at all such positions. In other words, for each point in \textbf{U}, there exists a circle of radius \textbf{r} that encircles that point and all the members of \textbf{C}. Your task is to calculate the length of the periphery of that region \textbf{U}. \textit{\textbf{Figure 1}}. shows an example of the set of circles \textbf{C} and the region \textbf{U}. In the gure, three circles contained in \textbf{C} are expressed by circles of solid circumference, some possible positions of the encircling circles are expressed by circles of dashed circumference, and the area \textbf{U} is expressed by a thick dashed closed curve. \includegraphics{https://static.e-olymp.com/content/34/345843c0fd2310bffa335efd4cfe8f78ab5c82ed.jpg} \textit{\textbf{Figure 1.}} Example of the Circle Set \InputFile The input is a sequence of datasets. The number of datasets is less than \textbf{100}. Each dataset is formatted as follows. \textbf{n r x_1 y_1 r_1 x_2 y_2 r_2 . . . x_n y_n r_n} The first line of a dataset contains two positive integers, \textbf{n} and \textbf{r}, separated by a single space. \textbf{n} means the number of the circles in the set \textbf{C} and does not exceed \textbf{100}. \textbf{r} means the radius of the encircling circle and does not exceed \textbf{1000}. Each of the \textbf{n} lines following the rst line contains three integers separated by a single space. (\textbf{x_i}, \textbf{y_i}) means the center position of the \textbf{i}^th circle of the set \textbf{C} and \textbf{r_i} means its radius. You may assume -\textbf{500} ≤ \textbf{x_i} ≤ \textbf{500}, -\textbf{500} ≤ \textbf{y_i} ≤ \textbf{500}, and \textbf{1} ≤ \textbf{r_i} ≤ \textbf{500}. The end of the input is indicated by a line containing two zeros separated by a single space. \OutputFile For each dataset, output a line containing a decimal fraction which means the length of the periphery (circumferential length) of the region \textbf{U}. The output should not contain an error greater than \textbf{0.01}. You can assume that, when \textbf{r} changes by \textbf{ϵ} (|\textbf{ϵ}| < \textbf{0.0000001}), the length of the periphery of the region \textbf{U} will not change more than \textbf{0.001}. If \textbf{r} is too small to cover all of the circles in \textbf{C}, output a line containing only \textbf{0.0}. No other characters should be contained in the output. \includegraphics{https://static.e-olymp.com/content/35/35cd782d4a64cfbe626f0635cc628e323184c2ed.jpg} \textit{\textbf{Figure 2}}. Last Dataset of the Sample Input