Goal
Products of several cosine and sine are hard to study, therefore, we go through a process of simplification. We simply replace every cos(x) with (e^(ix)+e^(-ix))/2 and every sin(x) with (e^(ix)-e^(-ix))/2i, with i² = -1; then we get rid of every cos/sin power by including them on the exponentials and we make the process the other way.
E.g. cos²(x) = ((e^(ix)+e^(-ix))/2)² = (e^(2ix) + 2 + e^(-2ix))/4, here we use once again the identity given above, => (cos(2x) + 1)/2
The goal here is to simplify an expression such as sin(x)^S * cos(x)^C * F, where F is a factor given such that the coefficients of the final sum are always integers.
Input
Three space separated integers S, C and F.
Output
A line with the answer formatted as k_0±k_1sin/cos(x)±k_2sin/cos(2x)±....
First the constant term then every term in ascending order of the coefficient in x within each sin/cos term.
If k = 0, the cos/sin associated need not be displayed.
Constraints
0 ≤ S ≤ 10
0 ≤ C ≤ 10
1 ≤ F ≤ 750,000
The output of such an expression will only contain sine or cosine, never both at the same time.
