Polygon

Time limit1sMemory limit256 MB

Summary

Sum the integers n between a and b for which some n-gon has all of its sides crossed by a single straight line.

Level: Medium7 of 10
Topics: Geometry, Math
Solved: No attempts yet

Problem

Seunghyun drew the figure below on a sheet of paper.

He noticed that for the quadrilateral at the bottom, a single straight line cuts all four sides.

That made him wonder how many sides such a polygon can have.

Write a program that adds up every $n$ for which an $n$ -gon exists whose sides can all be cut by one straight line. There are infinitely many such $n$ , so count only the ones with $n$ between $a$ and $b$ , inclusive. A polygon has at least three sides, so $n$ is at least 3.

Input

The first line contains two natural numbers $a$ and $b$ , separated by one space. ( $1 \le a \le b \le 10^9$ )

Output

Print the sum of every $n$ that satisfies the condition on the first line.

Examples3

Example 1
Input
```
3 4
```
Expected output
```
4
```
Example 2
Input
```
1 3
```
Expected output
```
0
```
Example 3
Input
```
5 10
```
Expected output
```
24
```