let x be an integer and let j be the sum of the digits of x. Subtract j from x and get x-j=y. Let k be the sum of the digits of y. Show that y-77,778j cannot equal 7,777,777.

I have tried to do this with divisibility criteria. For instance 77,778j must be even and 77,778 is divisible by 3 while 7,777,777 is not but the arbitrariness of x and y leave me stuck.