Problem Description

The Sieve of Eratosthenes is a well-known method for finding all prime numbers up to $n$. The steps of the algorithm are:

1. Write down all integers between $2$ and $n$ (including $2$ and $n$).
2. Find the smallest number that has not been deleted yet and name it $p$; then $p$ is a prime number.
3. Cross out $p$ and all of its multiples that have not been crossed out yet.
4. If there are still numbers not crossed out, go to step $2$.

Write a program that, given $n$ and $k$, finds the $k$-th integer that gets deleted.

Input Format

One line with two integers $n$ and $k$. Their meanings are described in the problem statement.

Output Format

Output one integer on one line, the $k$-th crossed-out integer.

7 3

6

15 12

7

10 7

9

Hint

Constraints

For $100\%$ of the testdata, $2 \leq k < n \leq 1000$.

Notes

Source

This problem is translated from COCI2008-2009 CONTEST #2 RESETO. Translator:

Translated by ChatGPT 5