Problem Description

The Sieve of Eratosthenes is a famous algorithm for finding all prime numbers up to $n$. The steps of the algorithm are:
1. Write down all integers from $2$ to $n$ (inclusive).
2. Find the smallest number that has not been deleted and name it $p$; $p$ is a prime number.
3. Cross out $p$ and all its multiples that have not been crossed out yet.
4. If there are still numbers that have not been crossed out, go to step 2.

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

Input Format

A single line containing two integers $n$ and $k$, as described in the problem statement.

Output Format

A single line containing one integer, representing the $k$-th integer that is crossed out.

Sample Input and Output

Sample Input #1

7 3

Sample Output #1

6

Sample Input #2

15 12

Sample Output #2

7

Sample Input #3

10 7

Sample Output #3

9

Notes

Data Size and Constraints

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

Translation

This problem is translated from COCI2008-2009 CONTEST #2 RESETO, translated by @mnesia.

见题面 Input 部分

见题面 Output 部分