element, 142 bytes

Result [link]

AC

Code [DL]

0 x;
0 y;
_ q;
100'[
  q~ ( 2 x~ * + x; q;
  2 y~ * y;
  x~ 1000000000000000 % tx;
  x~ tx~ -+ 1000000000000000 / y~ + y;
  tx~ x;
] 
y~`
x~`

stdin

1011010111010101100100110001111011001101101011100101000111100111100111111011001110110010110000111000

stdout

900399723733400815704196459576

stderr

strace