Excellent explanation, this helped me a lot, thankyou so much!!.
I read through the entire post and i could deduce the expression step by step :
if all elements are equal, say all elements are represented by min, then sum of all elements is :
len*min = sum
Now, say all elements are not equal, in that case, we keep adding 1 to each element, until it reaches max value.
say for ex : [1, 2, 3, 4]
step 1: 1 + 1 ( first elem)
step 2 : 2 + 1( first elem + 1)
step 3..... so on
hence left side expression becomes
len*(min + k) = sum + k * (len - 1)
lenmin + klen = sum + klen - k
lenmin = sum - k
k = sum - len*min