The sieve of Eratosthenes is a famous algorithm to find all prime numbers up to $N$. The algorithm is:
 - Write down all integers between 2 and $N$, inclusive.
 - Find the smallest number not already crossed out and call it $P$; $P$ is prime.
 - Cross out $P$ and all its multiples that aren’t already crossed out.
 - 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.

-----Input-----
The integers $N$ and $K$ $(1 \leq K < N \leq 100000)$.

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

-----Examples-----
Sample Input 1:
7 3
Sample Output 1:
6

Sample Input 2:
15 12
Sample Output 2:
7

Source: kattis | Difficulty: EASY
Tags: Mathematics


Solutions: