Turn Game

Time limit2sMemory limit512 MB

Summary

Given final scores x and y, decide whether some prefix of 1,2,3,... can be partitioned into two groups summing to x and y, and find the minimum count of terms in Yunho's group.

Level: Medium7 of 10
Topics: Math, Greedy, Binary search, Number theory
Solved: No attempts yet

Problem

Yunho and Donghyuk are at an algorithm camp. When a problem refuses to come out, the two of them play a game instead.

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

Given two integers $x$ and $y$ , write a program that decides whether the game can end with Yunho holding $x$ points and Donghyuk holding $y$ points. If it can, 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 no such game exists, print $-1$ .

Hint

If Yunho scores $7$ and Donghyuk scores $14$ , the game runs for $6$ turns. Yunho winning turns $1, 2, 4$ while Donghyuk wins turns $3, 5, 6$ is one possible result. Yunho wins the fewest turns when he takes turns $1$ and $6$ and Donghyuk takes turns $2, 3, 4, 5$ .

Examples4

Example 1
Input
```
7 14
```
Expected output
```
2
```
Example 2
Input
```
10 0
```
Expected output
```
4
```
Example 3
Input
```
932599670050 67400241741
```
Expected output
```
1047062
```
Example 4
Input
```
7 13
```
Expected output
```
-1
```