Feed Your Pigeon!

def checkio(number):
    def natural(n):
        return n * (n + 1) / 2;
    def iter(i, rest, acc):
        if not rest:
            return acc;
        pigeons = natural(i)
        eaten = min(rest, pigeons)
        return iter(i + 1, rest - eaten, max(acc, eaten))
    return iter(1, number, 0)