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Problem F
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The sieve of Eratosthenes is a famous algorithm to find all prime numbers up to $N$. The algorithm is:
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Write down all integers between 2 and $N$, inclusive.
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Find the smallest number not already crossed out and call it $P$; $P$ is prime.
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Cross out $P$ and all its multiples that aren’t already crossed out.
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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 $K$ $(1 \leq K < N \leq 100\, 000)$.
Output
Output the $K$-th number to be crossed out.
| Sample Input 1 | Sample Output 1 |
|---|---|
7 3 |
6 |
| Sample Input 2 | Sample Output 2 |
|---|---|
15 12 |
7 |
| Sample Input 3 | Sample Output 3 |
|---|---|
10 7 |
9 |