#!perl -p
for(;@s=@f=/1/;print@s){$a=s/0*.{@+}/"\$n=0b$&;1"/ee+s/.{$n}//;$a+=(@f=($a,@f))[1]until$a>eval'$v=0b'.$&;@s=(0+$v<=>($v%=$_),@s)for@f}