Problem C

The sieve of Eratosthenes is a famous algorithm to find all prime numbers up to $N$. The algorithm is:

  1. Write down all integers between 2 and $N$, inclusive.

  2. Find the smallest number not already crossed out and call it $P$; $P$ is prime.

  3. Cross out $P$ and all its multiples that aren’t already crossed out.

  4. If not all numbers have been crossed out, go to step 2.

Write a program that, given $N$ and $K$, find the $K$-th integer to be crossed out.


The integers $N$ and $K$ $(1 \leq K < N \leq 100\, 000)$.


Output the $K$-th number to be crossed out.

Sample Input 1 Sample Output 1
7 3
Sample Input 2 Sample Output 2
15 12
Sample Input 3 Sample Output 3
10 7
CPU Time limit 1 second
Memory limit 1024 MB
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Source Croatian Open Competition in Informatics 2008/2009, contest #2
License For educational use only

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