Project Euler #62: Cubic permutations

_{This problem is a programming version of Problem 62 from projecteuler.net}

The cube, , can be permuted to produce two other cubes: and .

In fact, is the smallest cube which has exactly three permutations of its digits which are also cube.

You are given , find the smallest cube for which exactly permutations of its digits are cube of some number which is . If there are multiple sets, print the minimal element of each in sorted order.

Input Format

Input contains two space separated integers and .

Constraints

Output Format

Print the answer corresponding to the test case. If there are more than one number, print them on separate lines.

Sample Input

1000 3

Sample Output

41063625