calculate the solution to  2^10000 * x = 1002773875431658367671665822006771085816631054109509173556585546508965236428620487083647585179992085437922318783218149808537210712780660412301729655917441546549321914516504576 mod 5^174
https://gist.github.com/yytasbag/9ab6c7d4a6e565e6fd29221fff1daf08