BALKAN-SL 2008 N1

Prove that for every natural number $a$ , there exists a natural number that has the number $a$ (the sequence of digits that constitute $a$ ) at its beginning, and which decreases $a$ times when $a$ is moved from its beginning to it end (any number zeros that appear in the beginning of the number obtained in this way are to be removed).

Example [list=i] [] $a=4$ , then $\underline{4}10256= 4 \cdot 10256\underline{4}$ [] $a=46$ , then $\underline{46}0100021743857360295716= 46 \cdot 100021743857360295716\underline{46}$