12.4.12 Various Olympiad problems

Problem: What is the sum of all numbers obtained from the number \( k \) by permuting the digits (including \( k \) ), if \( k=5307447 \) ? Representing 0 at the beginning of the number is not allowed. As an answer, write down the remainder of dividing the obtained sum by 10000 . If the question of the problem allows several answers, then indicate them all in the form of a set.