You are given two natural numbers N and K. You need to represent the number N as a product of K numbers such that all the K numbers are >= 2 and the sum of the K numbers is minimum. The constraints on the value of N <= 10^12. Given such values of K for which the answer always exist.

My Solution:- After finding the prime factorization of the number N. Insert the factors in a multiset and then solve the problem greedily. Take the first 2 elements of the multiset, remove them and then insert their product in the multiset. Keep on repeating this process until the size of multiset becomes equal to K.

I don't know whether the above approach is correct or not and also I am not sure whether the answer will be unique or not.

Any suggestions for the given approach or some new approach are welcomed.

UPD:- I know my approach is incorrect but still I am unable to figure out anything about uniqueness. Whether the answer will be unique or not.

Your solution is wrong; take

N= 36,K= 2.You can solve the problem in with DP.

EDIT: This might be too slow, depending on the test data.

Thanks for the reply!!! Can we say anything about the uniqueness of the K numbers?? If we take the numbers in sorted order will the answer be unique?

Any Updates???

Auto comment: topic has been updated by back_slash (previous revision, new revision, compare).