Go: package main

import (
	"bufio"
	"os"
	"strings"
	"strconv"
	"fmt"
)

var scanner = bufio.NewScanner(os.Stdin)

const INF = 0x7FFFFFFF

func main() {
	for scanner.Scan() {
		buf := strings.Split(scanner.Text(), " ")
		n, _ := strconv.Atoi(buf[0])
		m, _ := strconv.Atoi(buf[1])
		if n == 0 && m == 0 {
			break
		}
		chair := make([]string, n+1)
		for i := range chair {
			chair[i] = "#"
		}
		chair[n] = "Sentinel"
		for i := 0; i < m; i++ {
			scanner.Scan()
			switch who := scanner.Text(); who {
			case "A": // 左から眺めて行って空いている席があったら即座に座る
				for j := 0; j < n; j++ {
					if chair[j] == "#" {
						chair[j] = "A"
						break
					}
				}
				// log.Println(chair)
				break // 次の人を読み込む
			case "B":
				flag := true
				// 右端からAの隣でない席を探していく
				for j := n-1; j > -1; j-- {
					if chair[j] == "#" && (j == 0 || chair[j-1] != "A") && chair[j+1] != "A" {
						flag = false
						chair[j] = "B"
						break
					}
				}
				// Aの隣しか空いていないので一番左端の空いている席に座る
				if flag {
					for j := 0; j < n; j++ {
						if chair[j] == "#" {
							chair[j] = "B"
							break
						}
					}
				}
				// log.Println(chair)
				break // 次の人を読み込む
			case "C":
				if i == 0 {
					chair[n/2] = "C" // 先客が誰もいないときは真ん中の椅子に座る
				} else {
					for j := 0; j < n; j++ { // 左から舐めて
						if chair[j] != "#" { // その席が空いていなくて
							if chair[j+1] == "#" { // 右隣が空いているなら座る
								chair[j+1] = "C"
								break
							} else if j != 0 && chair[j-1] == "#" { // 右隣が空いていないので左隣に座る
								chair[j-1] = "C"
								break
							}
						}
					}
				}
				// log.Println(chair)
				break // 次の人を読み込む
			case "D":
				distanceTable := make([]int ,n)
				for j := range distanceTable {
					distanceTable[j] = INF
				}
				for j:= 0; j < n; j++ {
					if chair[j] != "#" {
						for k := 0; k < n; k++ {
							distanceTable[k] = min(distanceTable[k], abs(j-k))
						}
					}
				}
				// log.Println("distanceTAble:", distanceTable)
				at := 0
				distance := 0
				for j := 0; j < n; j++ {
					if distance < distanceTable[j] {
						at = j
						distance = distanceTable[j]
					}
				}
				chair[at] = "D"
				// log.Println(chair)
				break // 次の人を読み込む
			}
		}
		fmt.Println(strings.Join(chair[:len(chair)-1], ""))
	}
}

func min(a, b int) int {
	if a > b {
		return b
	}
	return a
}

func abs(a int) int {
	if a < 0 {
		return -a
	}
	return a
}

C++: #include <iostream>
#include <sstream>
#include <iomanip>
#include <algorithm>
#include <cmath>
#include <string>
#include <vector>
#include <list>
#include <queue>
#include <stack>
#include <set>
#include <map>
#include <bitset>
#include <numeric>
#include <climits>
#include <cfloat>
using namespace std;

int main()
{
    for(;;){
        int n, m;
        cin >> n >> m;
        if(n == 0)
            return 0;

        string s(n, '#');
        for(int i=0; i<m; ++i){
            char c;
            cin >> c;
            if(c == 'A'){
                *find(s.begin(), s.end(), '#') = 'A';
            }else if(c == 'B'){
                bool ok = false;
                for(int j=n-1; j>=0; --j){
                    if(s[j] != '#')
                        continue;
                    if(j+1 < n && s[j+1] == 'A')
                        continue;
                    if(j-1 >= 0 && s[j-1] == 'A')
                        continue;
                    s[j] = 'B';
                    ok = true;
                    break;
                }
                if(!ok)
                    *find(s.begin(), s.end(), '#') = 'B';
            }else if(c == 'C'){
                if(i == 0){
                    s[n/2] = 'C';
                }else{
                    for(int j=0; j<n; ++j){
                        if(s[j] != '#'){
                            if(j+1 < n && s[j+1] == '#'){
                                s[j+1] = 'C';
                                break;
                            }else if(j-1 >= 0 && s[j-1] == '#'){
                                s[j-1] = 'C';
                                break;
                            }
                        }
                    }
                }
            }else{
                if(i == 0){
                    *find(s.begin(), s.end(), '#') = 'D';
                }else{
                    vector<int> dist(n, INT_MAX);
                    for(int j=0; j<n; ++j){
                        if(s[j] == '#')
                            continue;
                        int k = j;
                        do{
                            dist[k] = min(dist[k], j - k);
                        }while(--k >= 0 && s[k] == '#');
                        k = j;
                        do{
                            dist[k] = min(dist[k], k - j);
                        }while(++ k < n && s[k] == '#');
                    }
                    s[max_element(dist.begin(), dist.end()) - dist.begin()] = 'D';
                }
            }
        cout << s << endl;
        }

    }
}

C++: #include<iostream>
#include<algorithm>
const int infty = 1<<28;
using namespace std;
int main()
{
  while(true){
    int n,m;
    cin >> n >> m;
    if( n == 0 && m == 0 ) break;
    char C[n+2];
    fill(C,C+n+2,'#');

    //cout << " ---------- " << endl;
    for(int p = 0; p < m; ++p){
      char c;
      cin >> c;
      /*for(int i = 1; i < 1+n; ++i){
	cout << C[i];
      }
      cout << endl;
      */
      if(c=='A'){
	for(int i = 1; i < 1+n; ++i){
	  if( C[i] == '#' ){
	    C[i] = 'A';
	    break;
	  }
	}
      }else if(c=='B'){
	bool sc=false;
	for(int i = n; i >= 1; --i){
	  if( C[i] == '#' && C[i-1] != 'A' && C[i+1] != 'A' ){
	    C[i] = 'B';
	    sc=true;
	    break;
	  }
	}
	if(!sc){
	  for(int i = 1; i < n+1; ++i){
	    if( C[i] == '#' ){
	      C[i] = 'B';
	      break;
	    }
	  }
	}
      }else if(c=='C'){
	bool sc = false;
	for(int i = 1; i < 1+n; ++i){
	  if( C[i] != '#' ){
	    if( C[i+1] != '#' ){
	      if( C[i-1] != '#' ){
		continue;
	      }else{
		C[i-1] = 'C';
		sc=true;
		break;
	      }
	    }else{
	      C[i+1] = 'C';
	      sc=true;
	      break;
	    }
	  }
	}
	if( !sc ){
	  if( n % 2 == 0 ){
	    C[ n/2 + 1 ] = 'C';
	  }else{
	    C[ (n+1)/2 ] = 'C';
	  }
	}
      }else if(c=='D'){
	int max_dist = -1;
	int nearest_dist[n+2];
	fill(nearest_dist,nearest_dist+n+2,infty);
	bool empty=true;
	for(int i = 1; i < 1+n; ++i){
	  if( C[i] != '#' ) empty=false;
	}
	if(empty){C[1]='D';continue;}
	
	for(int i = 1; i < 1+n; ++i){
	  if( C[i] != '#' ) continue;
	  int min_right = infty, min_left = infty;
	  for(int j = i - 1; j >= 1; --j){
	    if( C[j] != '#'){
	      min_left = i - j - 1;
	      break;
	    }
	  }
	  for(int j = i + 1; j < 1+n; ++j){
	    if( C[j] != '#' ){
	      min_right = j - i - 1;
	      break;
	    }
	  }

	  nearest_dist[i] = min( min_right, min_left );
	  max_dist = max( max_dist, nearest_dist[i] );
	}
	for(int i = 1; i < i+n; ++i){
	  //cout << nearest_dist[i] << ' ' << max_dist << endl;
	  if( nearest_dist[i] == max_dist ){
	    C[i] = 'D';
	    break;
	  }
	}
      }
    }
    for(int i = 1; i < 1+n; ++i){
      cout << C[i];
    }
    cout << endl;
  }
  return 0;
}