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, A_i, ω_i, and φ_i 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 ≤ A_i ≤ 10, 0 ≤ ω_i ≤ 100 and 0 ≤ φ_i ≤ 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

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