rail, 1686 bytes

Result [link]

AC

Code [DL]

$ 'dup' (a -- a a)
 \
  \-(!store!)--(store)-(store)-#

$ 'is_all_zero_list' (a -- b)
 \
 | /-------------\
 |/              |
 |               /
 \          /-~-<
  \-{dup}nq<     \-(!a!)-0-#
            \
             \-(!a!)-1-#

$ 'is_all_zero' (a -- b)
 \                                /-1c(!a!)(!b!)(a){is_all_zero}-#
 |            /-{dup}0{get_str_i}<
 \-{dup}[]q--<                    \-(!a!)0-#
              \-(!a!)1-#


$ 'get_str_i' (a b -- c)
 \
  \-c1c(!c!)(!c!)(!e!)(c)-#

$ 'set_str_i' (a b c -- d)
 \
  \-(!c!)c1c(!d!)(!e!)(c)p(d)p-#

$ 'input' (-- a)
 \
 |     /--\
 |    /    >-g0(n)(!n!)-\
 |    | #-/             |
 |    \                 |
 |     \-----\          |
 |            \         |
 \-[100](!n!)[]-ip(n)1s-/

$ 'o' (a -- a)
 \
  \-{dup}o[\n\]o-#

$ 'main'
 \
  \-{input}(!bin!)-\               /-(!ced!)o~(ced)-\
                   |               |                |
 /-------(!ced!)n--/               \                /
 |                                /--(dec)-------nq<
 \--0(!j!)(bin){is_all_zero}---0q<                  \-#
  /                               \
  |                                \-0(!rem!)--(rem)2m(bin)---(j)---{get_str_i}a(!rem!)(bin)(j)(rem)[10]d-\
  |                                          /                                                            |
  |                                          |                                                            |
  |                                          \                                                            |
  |                                           >g(j)[001](!j!)a1(j)(!mer!)r[01](mer)(!nib!)---{i_rts_tes}--/
  \-(!ced!):(mer)(ced)-----------------------/

stdin

1001101011101100110000010100010011101011111001110000101100111011011110101110010011000001111001001001

stdout

767150571104392825459979329097

stderr

strace