Easy Sequence Sum

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Time limit2sMemory limit128 MB

Summary
Given a sequence where each integer k repeats k times, compute the sum of terms between positions A and B.
Level

Easy2 of 10

Topics
Math, Simulation, Implementation
Solved
No attempts yet

Problem

Consider the following sequence. The number 1 appears once, 2 appears twice, 3 appears three times, and in general each positive integer k appears exactly k consecutive times.

1 2 2 3 3 3 4 4 4 4 5 ...

Given an interval [A, B], compute the sum of the terms from the A-th term through the B-th term of this sequence.

Input

The first line contains two integers A and B, the start and end positions of the interval.

1 <= A <= B <= 1,000

Output

Print the sum of the terms in the interval.

Examples1

  1. Example 1

    Input
    3 7
    Expected output
    15