Turn Game 2

Time limit2sMemory limit512 MB

Summary

Decide whether turn wins of weights 1, 3, 5, ... can give Yunho x and Donghyeok y points, minimizing Yunho's wins.

Level: Medium5 of 10
Topics: Math, Greedy, Number theory
Solved: No attempts yet

Problem

Yunho and Donghyeok are at an algorithm camp. When a problem will not come out, they take a break and play a game.

The game is made of turns, and each turn is won by one of the two players. Turns are numbered from 1, and the winner of turn $i$ earns $2i-1$ points.

The total number of turns is not fixed. Any number of turns is possible, including zero.

You are given two integers $x$ and $y$ . Decide whether Yunho can end with $x$ points and Donghyeok with $y$ points. If that is possible, also find the smallest number of turns Yunho has to win.

Input

The first line contains two integers $x$ and $y$ . ( $0 \le x, y \le 10^{12}$ )

Output

Print the smallest number of turns Yunho has to win. If scores $x$ and $y$ are impossible, print -1.

Examples5

Example 1
Input
```
8 17
```
Expected output
```
2
```
Example 2
Input
```
17 8
```
Expected output
```
3
```
Example 3
Input
```
0 0
```
Expected output
```
0
```
Example 4
Input
```
9 9
```
Expected output
```
-1
```
Example 5
Input
```
500000 500000
```
Expected output
```
294
```