My assumption is that radix sort is somehow involved.
The result is also in the attached file, which is of the same content as the follows:
Let us use the following example to facilitate the explanation:
In this example, the number of digits is 56, i.e., n = 56
Let m be the number of numbers, i.e., m = 15 in this example, then m < n
Let n1, n2, ... nk are the possible number of digits of each number in the array, so in this example,
n1 = 1, n2=2, n3 = 3, n4 = 4, n5 = 5, n6 = 6, ...
This job targets sorting an array of integers in linear time.