Heeju's Math Exam

Time limit1sMemory limit128 MB

Summary

Sum the terms from position A to B in the sequence where each integer k appears k times in a row.

Level: Easy2 of 10
Topics: Simulation, Implementation
Solved: No attempts yet

Problem

An integer sequence is built by the following rule: 1 appears once, 2 appears twice, 3 appears three times, …, that is, the integer $k$ appears $k$ times in a row. So the sequence begins like this.

$1,\ 2,\ 2,\ 3,\ 3,\ 3,\ 4,\ 4,\ 4,\ 4,\ 5,\ \dots$

Given two integers $A$ and $B$ , compute and print the sum of all values from the $A$ -th term to the $B$ -th term of this sequence, inclusive.

Input

A single line contains two integers $A$ and $B$ separated by a space. ( $1 \le A \le B \le 1000$ )

Output

Print, on one line, the sum of the terms from the $A$ -th to the $B$ -th.

Examples3

Example 1
Input
```
1 3
```
Expected output
```
5
```
Example 2
Input
```
3 7
```
Expected output
```
15
```
Example 3
Input
```
50 50
```
Expected output
```
10
```