Given two integer N and K, the task is to find the permutation P of first N natural numbers such that there are exactly K elements which satisfies the condition GCD(P[i], i) > 1 for all 1 ≤ i ≤ N.
Input: N = 3, K = 1
Output: 2 1 3
GCD(P, 1) = GCD(2, 1) = 1
GCD(P, 2) = GCD(1, 2) = 1
GCD(P, 3) = GCD(3, 3) = 3
There is exactly 1 element such that GCD(P[i], i) > 1
Input: N = 5, K = 2
Output: 3 1 2 4 5
Approach: Keep the last K elements in their place. The rest of the elements are moved such that ith element is placed in (i + 1)th position and (N – K)th element is kept in position 1 because gcd(x, x + 1) = 1.
Below is the implementation of the above approach:
3 1 2 4 5
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