Sum and Product

Time limit2sMemory limit128 MB

Summary

Given a sum S and a product P, find the smallest list of nonnegative reals whose sum is S and product is P, or report -1 if impossible.

Level: Medium6 of 10
Topics: Math, Binary search
Solved: No attempts yet

Problem

Consider a list of nonnegative numbers. If the sum of all numbers in the list is S and their product is P, call the list valid.

Given S and P, find the minimum possible size of a valid list. The size of a list is the number of numbers it contains. If no such list exists, print -1.

The numbers in the list are not required to be integers.

Input

The first line contains two natural numbers S and P, separated by a space. Each number is at most 1,000,000,000.

Output

Print the answer on the first line.

Examples4

Example 1
Input
```
5 6
```
Expected output
```
2
```
Example 2
Input
```
10 10
```
Expected output
```
1
```
Example 3
Input
```
5 100
```
Expected output
```
-1
```
Example 4
Input
```
100 1000000000
```
Expected output
```
9
```