I am trying to find a way to obtain the last 3 digits of k,

where k = 4321^(10^4321 + 1).

I can see that 10^4321 + 1 = log(k) / log(4321),

or log(k) / log(4321) - 10^4321 = 1

However, numbers are so huge here that I think the use of

some trick or theory is required.

Can anyone help. Thank you.