Do It

Time Limit : 8 sec, Memory Limit : 65536 KB

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Problem G: Do It

There is sometimes difficulty giving nice backgrounds to contest problems. So let this problem kept this simple - write a program that calculates the value of the following formula where the parameters N, R, Ai, ωi, and φi are all given:

Input

The input consists of a series of datasets each of which has the following format:

      N R
      A1 ω1 φ1
      A2 ω2 φ2
      ...
      AN ωN φN

The numbers in the input are all integers and satisfy the following conditions: 1 ≤ N ≤ 16, 1 ≤ R ≤ 104, 1 ≤ Ai ≤ 10, 0 ≤ ωi ≤ 100 and 0 ≤ φi ≤ 360.

The end of input is indicated by N = R = 0. This is not part of any dataset and hence should not be processed.

Output

For each dataset, print the result of the integration in a line. The result may be printed with an arbitrary number of fractional digits, but should have a relative or absolute error not greater than 10-8.

Sample Input

1 1
1 1 0
0 0

Output for the Sample Input

0.45969769413186

Source: ACM-ICPC Japan Alumni Group Summer Camp 2008 , Day 4, Tokyo, Japan, 2008-09-15
http://acm-icpc.aitea.net/