String-zip

You must be familiar with zip compression. It compresses files to a certain ratio. Hmm interesting, isn’t it? But what about strings? Can we write a program to compress them too? Lets write a program to compress any string of length $n$ to string with minimum possible length, such that the compressed string can be repeated $t$ times to form the original string, where $1$ ≤ $t$ ≤ $n$. Lets take