Competitions

# DSLCS 2011 Number Theory. Favorites

# Sum And Product

A list of non-negative numbers is called satisfactory if the sum of the numbers in the list is equal to **s** and the product of the numbers is equal to **p**. Find a satisfactory list with the least possible number of elements.

#### Input

Each line is a separate test that contains two non-negative integers **s** and **p** (**1** ≤ **s**, **p** ≤ `10`

).^{9}

#### Output

For each test case print in a separate line the size of satisfactory list with the least possible number of elements. If no such list exists, print **-1** instead. Please note that the list may contain non-integer numbers.

Input example #1

10 10 5 6 5 100

Output example #1

1 2 -1