22678번 - Do It 스페셜 저지다국어

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:

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

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.

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.