Find The Pivot Integer · Interview Problem

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Leetcode

Easy

Math

Number Theory

Find The Pivot Integer

Find an integer x such that the sum of numbers from 1 to x equals the sum of numbers from x to n.

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Problem Statement

Given a positive integer n, find the pivot integer x such that:

the sum of all integers from 1 to x is equal to
the sum of all integers from x to n

If such an integer exists, return it. Otherwise, return -1.

A pivot integer is allowed to be any integer in the range [1, n].

Input Format

A single integer n.

You may assume n >= 1.

Output Format

Return the pivot integer x if one exists.
Otherwise, return -1.

Constraints

$1 \le n$
The answer, if it exists, is an integer in the range $[1, n]$ .

Examples

Sample cases returned by the problem API.

Example 1

Input

n = 8

Output

Explanation

Sum from 1 to 6 is 21, and sum from 6 to 8 is also 21. So the pivot integer is 6.

Example 2

Input

n = 4

Output

-1

Explanation

No integer x in [1, 4] makes the sum from 1 to x equal the sum from x to 4.

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