var
  n: integer;
  s: string;

  function Go(s: string): string;
   var
    sum: integer;
    i: integer;
    j: integer;
    stmp: string;
    tmp: integer;
   begin
    s:=trim(s);

    sum:=0;
    for i:=1 to length(s) do
     if s[i]='1' then sum:=sum+i;

    if (length(s)=n) and (sum mod (n+1) = 0) then
                              begin
                               result:=s;
                               exit;
                              end;

   if (length(s)=n-1) then
                       begin
                        if sum mod (n+1) = 0 then
                            result:=s+'0' else
                            result:=s+'1';
                        exit;
                       end;

   if (length(s)=n+1) then
                        begin
                         for i:=1 to length(s) do
                          begin
                          stmp:=s;
                          Delete(stmp,i,1);
                          tmp:=0;

                          for j:=1 to length(stmp) do
                           if stmp[j]='1' then tmp:=tmp+j;

                           if tmp mod (n+1) = 0 then
                             begin
                              result:=stmp;
                              exit;
                             end;
                          end;
                        end;
   for i:=length(s) downto 1 do
    if (s[i]='1') then
        if
        ((sum-i) mod (n+1) = 0)
        then begin s[i]:='0'; break; end else
    else if ((sum+i) mod (n+1) = 0)
        then begin s[i]:='1'; break; end;
    result:=s;
   end;

begin
//  assign(input,'input.txt'); reset(input);

  readln(n);

  while not eof do
   begin
    readln(s);

    writeln(Go(s));
   end;

 // sleep(12121);
end.

see also this (or give more test data):

#include <iostream>
#include <string>

using namespace std;

short N;
char word[2001][1001];

int main(){
    int i=0,j,n,s=0,c=0,temp;
    cin>>N;
    while(cin>>word[i])i++;
    n=i;
    for(i=0;i<n;i++){
////////////////////// CASE 1 (REPLACED)//////////////////////
        if(strlen(word[i])==N){
            for(j=0;j<N;j++)
                if(word[i][j]=='1')s+=j+1;
            s%=(N+1);
            word[i][s-1]='0';
        }
////////////////////// CASE 2 (REMOVED)//////////////////////
        else if(strlen(word[i])==N-1){
            for(j=0;j<N-1;j++)
                if(word[i][j]=='1'){
                    s+=j+1;
                    c++;
                }
            s%=(N+1);
            if(s!=0)s=N+1-s;
            if(s<=c){    // Removed '0'
                for(j=N-2;s!=0;j--){
                    word[i][j+1]=word[i][j];
                    if(word[i][j]=='1')s--;
                }
                word[i][j+1]='0';
            }
            else {    // Removed '1'
                short mod=s;
                c=0;
                for(j=s;j<N-1;j++)
                    if(word[i][j]=='1')c++;
                while(s+c!=mod){
                    s--;
                    if(word[i][s-1]=='1')c++;
                }
                for(j=N-1;j>=s;j--)word[i][j]=word[i][j-1];
                word[i][s-1]='1';
            }
        }
////////////////////// CASE 3 (INSERTED)//////////////////////
        else if(strlen(word[i])==N+1){
            for(j=0;j<N+1;j++)
                if(word[i][j]=='1')s+=(j+1);
            s%=(N+1);
            for(j=N;j>=0 && c!=s;j--)
                if(word[i][j]=='1')c++;
            if(j>=0 && word[i][j]=='0'){ // Inserted '0'
                for(;j<N;j++)word[i][j]=word[i][j+1];
                word[i][j]=0;
            }
            else {    // Inserted '1'
                if(s==0)s=N+1;
                short mod=s;
                c=0;
                for(j=s;j<N+1;j++)
                    if(word[i][j]=='1')c++;
                while(s+c!=mod){
                    s--;
                    if(word[i][s]=='1')c++;
                }
                for(j=s-1;j<N+1;j++)word[i][j]=word[i][j+1];
                word[i][j]=0;
            }
        }
        s=c=0;
    }
    for(i=0;i<n;i++)cout<<word[i]<<endl;
    return 0;
}