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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def simplex_iterator(scale, boundary=True):
 """ Systematically iterates through a lattice of points on the 2-simplex. Parameters scale: Int The normalized scale of the simplex, i.e. N such that points (x,y,z) satisify x + y + z == N boundary: bool, True Include the boundary points (tuples where at least one coordinate is zero) Yields ------ 3-tuples, There are binom(n+2, 2) points (the triangular number for scale + 1, less 3*(scale+1) if boundary=False """


    start = 0
    if not boundary:
        start = 1
    for i in range(start, scale + (1 - start)):
        for j in range(start, scale + (1 - start) - i):
            k = scale - i - j
            yield (i, j, k)