Given an integer N. Print the count of permutations for the numbers from 1 to N, considering that prime numbers should be placed at positions with prime indices (1 - based indexing). As the result might be a large number, print the output % 1e9 + 7.
Question
Given an integer N. Print the count of permutations for the numbers from 1 to N, considering that prime numbers should be placed at positions with prime indices (1 - based indexing). As the result might be a large number, print the output % 1e9 + 7.
Solution
This problem can be solved using combinatorics and dynamic programming. Here are the steps:
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First, we need to find the prime numbers from 1 to N. We can use the Sieve of Eratosthenes algorithm for this. This algorithm will give us all the prime numbers up to N.
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Next, we need to count the number of prime numbers and the number of non-prime numbers. We also need to count the number of prime indices and non-prime indices.
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We then calculate the number of permutations of prime numbers at prime indices. This can be done using the formula for permutations: nPr = n! / (n-r)!, where n is the number of prime numbers and r is the number of prime indices.
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Similarly, we calculate the number of permutations of non-prime numbers at non-prime indices.
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The total number of permutations is the product of the permutations of prime numbers at prime indices and the permutations of non-prime numbers at non-pr
Similar Questions
Input FormatThe first and only line of input contains an integer N.Output FormatPrint the count of permutations.
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