K-th Prime Number

Given an integer k, your task is to output the k-th smallest prime number. Let \(P_n\) denote the n-th prime number. That is, for a valid input k (with \(k \ge 1\) and \(k\) not exceeding the total number of primes precomputed up to \(10^6\)), you should print \(P_k\). If k is not valid, output None.

Note: Primes are computed using the sieve of Eratosthenes up to \(10^6\). Use standard input/output for reading the input and writing the output.

inputFormat

The input consists of a single integer k provided via standard input.

outputFormat

If k is valid, output the k-th smallest prime number to standard output. Otherwise, output None (without quotes).

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