Split Array into Fibonacci Sequence — Python

# Time:  O(n^3)
# Space: O(n)


class Solution(object):
    def splitIntoFibonacci(self, S):
        """
        :type S: str
        :rtype: List[int]
        """
        def startswith(S, k, x):
            y = 0
            for i in xrange(k, len(S)):
                y = 10*y + int(S[i])
                if y == x:
                    return i-k+1
                elif y > x:
                    break
            return 0

        MAX_INT = 2**31-1
        a = 0
        for i in xrange(len(S)-2):
            a = 10*a + int(S[i])
            b = 0
            for j in xrange(i+1, len(S)-1):
                b = 10*b + int(S[j])
                fib = [a, b]
                k = j+1
                while k < len(S):
                    if fib[-2] > MAX_INT-fib[-1]:
                        break
                    c = fib[-2]+fib[-1]
                    length = startswith(S, k, c)
                    if length == 0:
                        break
                    fib.append(c)
                    k += length
                else:
                    return fib
                if b == 0:
                    break
            if a == 0:
                break
        return []