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문제

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 NRAiωi, and φi are all given:

$$ \int_{0}^{R}{\left[\prod_{i=1}^{N}{A_i \sin{\left( ω_it + φ_i \cdot \frac{\pi}{180} \right)}}\right]dt} $$

입력

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.

출력

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.

예제 입력 1

1 1
1 1 0
0 0

예제 출력 1

0.45969769413186