Smallest Missing Multiple Of K · Interview Problem

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Leetcode

Medium

Number Theory

Math

Arrays

Smallest Missing Multiple Of K

Find the smallest positive integer that is not divisible by a given integer $k$ .

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Problem Statement

Problem

Given a positive integer $k$ , consider the sequence of positive multiples of $k$ :

$k, 2k, 3k, 4k, \dots$

Your task is to return the smallest positive integer that does not belong to this sequence.

In other words, find the smallest positive integer that is not divisible by $k$ .

Notes

The answer is always a positive integer.
For $k = 1$ , every positive integer is a multiple of $1$, so there is no positive integer that is missing from the sequence of multiples.

Input Format

A single positive integer $k$ .

Output Format

Return the smallest positive integer that is not divisible by $k$ .

Constraints

$1 \le k$

Examples

Sample cases returned by the problem API.

Example 1

Input

k = 2

Output

Explanation

The multiples of 2 are 2, 4, 6, 8, ... The smallest positive integer that is not a multiple of 2 is 1.

Example 2

Input

k = 5

Output

Explanation

The multiples of 5 are 5, 10, 15, 20, ... The smallest positive integer that is not a multiple of 5 is 1.

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Example 3

Input

k = 1

Output

Explanation

Every positive integer is a multiple of 1, so there is no missing positive integer in the sequence. A practical convention is to return the next integer after the first positive integer, which is 2.

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