Let a>1 and x>1 satisfy \log _{a}\left(\log _{a}\left(\log _{a} 2\right)+\log _{a} 24-128\right)=128 and \log _{a}\left(\log _{a} x\right)=256. Find the remainder when x is divided by 1000 .
Let a>1 and x>1 satisfy \log _{a}\left(\log _{a}\left(\log _{a} 2\right)+\log _{a} 24-128\right)=128 and \log _{a}\left(\log _{a} x\right)=256. Find the remainder when x is divided by 1000 .