想见面不容易

<p> <span style="color:#E53333;font-size:14px;"><strong>之前的中文题意与测试数据有歧义，现把题目内容改为英文原题。</strong></span> </p> <p> <br /> </p> <p> Xiaoming lives in a village but his girl friend lives in another village. He decided to follow the straight path between his house (A) and girl friend's&nbsp;house (B), but there are several rivers he needs to cross. Assume B is to the right of A, and all the rivers lie&nbsp;between them.&nbsp; </p> &nbsp;<br /> Fortunately, there is one "automatic" boat moving smoothly in each river. When he arrives the left bank of a river, just&nbsp;wait for the boat, then go with it. He is so slim that carrying him does not change the speed of any boat.&nbsp;<br /> &nbsp;<br /> Days and days after, he came up with the following question: assume each boat is independently placed at random at&nbsp;time 0, what is the <span style="color:#E53333;"><strong>expected time</strong></span> to reach B from A? His walking speed is always 1.&nbsp;<br /> &nbsp;<br /> To be more precise, for a river of length L, the distance of the boat (which could be regarded as a mathematical point) to&nbsp;the left bank at time 0 is <span style="color:#E53333;"><strong>uniformly chosen</strong></span> from interval [0, L], and the boat is equally like to be moving left or right, if&nbsp;it’s not precisely at the river bank.<br />

There will be at most 10 test cases. Each case begins with two integers n and D, where n (0&lt;=n&lt;=10) is the number of rivers&nbsp;between A and B, D (1&lt;=D&lt;=1000) is the distance from A to B. Each of the following n lines describes a river with 3&nbsp;integers: p, L and v (0&lt;=p&lt;D, 0&lt;L&lt;=D, 1&lt;=v&lt;=100). p is the distance from A to the left bank of this river, L is the length of&nbsp;this river, v is the speed of the boat on this river. It is guaranteed that rivers lie between A and B, and they don’t overlap.&nbsp;<br /> The last test case is followed by n=D=0, which should not be processed.

For each test case, print the case number and the expected time, rounded to 3 digits after the decimal point.&nbsp;<br /> Print a blank line after the output of each test case.