Equal-Sum Split Point

Easy

The numbers from 1 to n are written in a row. Find a number x from that row such that the sum of all numbers from 1 to x equals the sum of all numbers from x to n (x itself counts in both sums). Return x, or -1 if there is no such number. When x exists, it is unique.

Example 1

n=49 → 35

1 + 2 + … + 35 = 630 and 35 + 36 + … + 49 = 630.

Example 2

n=5 → -1

No x from 1 to 5 works: for example, x = 4 gives 10 on the left and 9 on the right.

Example 3

n=1 → 1

Constraints

1 ≤ n ≤ 1000

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Topics

Math Prefix Sum

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Input

n=49

Expected

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