For a given positive integer m, a positive number is called a m-number if the product of its digits is m. For example, the beginning of a series of 24-numbers are as follows: 38, 46, 64, 83, 138, 146, 164, 183, 226 ...

You are given a positive integer m and k. Print k-th among m-numbers if all m-numbers are sorted in ascending order.

Input

A single line of input contains two integers m and k (2 ≤ m ≤ 10^9, 1 ≤ k ≤ 10^9).

Output

Print the desired number — k-th among all m-numbers if m-numbers are sorted in ascending order. If the answer does not exist, print -1.

Examples

Input


24 9


Output


226


Input


24 1


Output


38


Input


5040 1000000000


Output


111121111315213227111


Input


2020 2020


Output


-1

Source: codeforces | Difficulty: UNKNOWN_DIFFICULTY
Tags: Dynamic programming

Mathematics


Solutions: