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.

Examples