Background

Translated from POI2021~2022R2 Day1T2。

Problem Description

Define the “unfriendly numbers” $b$ of $a$ as the numbers satisfying $\gcd(a,b)=1$。

Now you are given the number $n$。You need to output the $c$ numbers starting from the $k$-th number in the increasing order of its “unfriendly numbers”。

Input Format

One line with three numbers $n,k,c\ (2 \leq n \leq 10^{14}, 1 \leq k \leq 10^{14}, 1 \leq c \leq 10^5)$。

Output Format

Output $c$ numbers, representing the $k \sim k+c-1$-th “unfriendly numbers” of $n$。

10 3 4

7 9 11 13

Hint

Explanation of the sample：

The “unfriendly numbers” of $10$ are $1,3,7,9,11,13,17\ldots$ in order。

The subtasks are as follows：

Here, $M$ is the maximum value in the output, and $f(n)$ is the count of “unfriendly numbers” $\leq n$。

Translated by ChatGPT 5