Problem: A parking lot in the City consists of n parking spaces, standing in a line. The parking spaces are numbered from 1 to n from left to right. 

When a car arrives at the lot, the operator determines an empty parking space for it. For the safety's sake the chosen place should be located as far from the already occupied places as possible. That is, the closest occupied parking space must be as far away as possible. If there are several such places, then the operator chooses the place with the minimum index from them. If all parking lot places are empty, then the car gets place number 1.

We consider the distance between the i-th and the j-th parking spaces equal to 4·|i - j| meters.

You are given the parking lot records of arriving and departing cars in the chronological order. For each record of an arriving car print the number of the parking lot that was given to this car.

Input

The first line contains two space-separated integers n and m (1 ≤ n, m ≤ 2·105) — the number of parking places and the number of records correspondingly. 

Next m lines contain the descriptions of the records, one per line. The i-th line contains numbers ti, idi (1 ≤ ti ≤ 2; 1 ≤ idi ≤ 106). If ti equals 1, then the corresponding record says that the car number idi arrived at the parking lot. If ti equals 2, then the corresponding record says that the car number idi departed from the parking lot. 

Records about arriving to the parking lot and departing from the parking lot are given chronologically. All events occurred consecutively, no two events occurred simultaneously.

It is guaranteed that all entries are correct: 

  * each car arrived at the parking lot at most once and departed from the parking lot at most once, 
  * there is no record of a departing car if it didn't arrive at the parking lot earlier, 
  * there are no more than n cars on the parking lot at any moment. 



You can consider the cars arbitrarily numbered from 1 to 106, all numbers are distinct. Initially all places in the parking lot are empty.

Output

For each entry of an arriving car print the number of its parking space. Print the numbers of the spaces in the order, in which the cars arrive to the parking lot.

Examples

Input

7 11
1 15
1 123123
1 3
1 5
2 123123
2 15
1 21
2 3
1 6
1 7
1 8


Output

1
7
4
2
7
4
1
3

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class ParkingLot implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    public static void main(String[] args) {
        new ParkingLot().run();
    }

    public void run() {
        try {
            long t1 = System.currentTimeMillis();
            if (System.getProperty("ONLINE_JUDGE") != null) {
                in = new BufferedReader(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                in = new BufferedReader(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }
            Locale.setDefault(Locale.US);
            solve();
            in.close();
            out.close();
            long t2 = System.currentTimeMillis();
            System.err.println("Time = " + (t2 - t1));
        } catch (Throwable t) {
            t.printStackTrace(System.err);
            System.exit(-1);
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    // solution

    public class Interval implements Comparable {
        int start;
        int end;
        int size;
        int nextPlace;

        public Interval(int start, int end) {
            this.start = start;
            this.end   = end;
            this.size = 0;
            this.nextPlace = -1;
            int realsize = end - start - 1;
            if(realsize > 0){
                if(start != 0 && end != n + 1){
                    this.size = 1 + (realsize-1)/2;
                    this.nextPlace = start + this.size;
                }
                else if(start == 0) {
                    this.size = end - 1;
                    this.nextPlace = 1;
                }
                else {
                    this.nextPlace = n;
                    this.size = n - start;
                }
            }
        }


        @Override
        public int compareTo(Object o) {
            Interval to = (Interval) o;
            int ret = (to.size - this.size);
            if(ret != 0)
                return ret;
            return(this.start - to.start);
        }
    }


    TreeSet<Interval> pq = new TreeSet<Interval>();
    Map<Integer,Interval> startMap = new HashMap<Integer,Interval>();
    Map<Integer,Interval> endMap   = new HashMap<Integer, Interval>();
    Map<Integer,Integer>  carMap  = new HashMap<Integer, Integer>();
    int n ;
    int m;

    void add(Interval interval) {
        pq.add(interval);
        startMap.put(interval.start, interval);
        endMap.put(interval.end, interval);
    }

    Interval remove(Interval it) {
        pq.remove(it);
        startMap.remove(it.start);
        endMap.remove(it.end);
        return it;
    }


    void solve() throws IOException {
        n = readInt();
        m = readInt();
        Interval it = new Interval(0, n+1);
        add(it);
        for(int i = 0 ; i < m; i ++) {
            int action = readInt();
            int car    = readInt();
            if(action == 1) {
                Interval interval= pq.first();
                pq.remove(interval);
                remove(interval);
                out.println(interval.nextPlace);
                carMap.put(car, interval.nextPlace);
                Interval left = new Interval(interval.start,  interval.nextPlace);
                Interval right =new Interval(interval.nextPlace, interval.end);
                add(left);
                add(right);
            }
            else {
                int place = carMap.remove(car);
                Interval left = endMap.get(place);
                Interval right = startMap.get(place);
                remove(left);
                remove(right);
                Interval interval = new Interval(left.start, right.end);
                add(interval);
            }
        }

    }

}