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 E implements Runnable {
    private MyScanner in;
    private PrintWriter out;

    int n;

    private void solve() {
        n = in.nextInt();
        int m = in.nextInt();
        TreeSet<Interval> tree = new TreeSet<>();
        tree.add(new Interval(1, n));
        final int MAXID = 1000000;
        int[] placeById = new int[MAXID + 1];
        Interval[] starts = new Interval[MAXID + 1], ends = new Interval[MAXID + 1];
        boolean[] used = new boolean[n + 1];
        for (int i = 0; i < m; ++i) {
            int t = in.nextInt(), id = in.nextInt();
            if (t == 1) {
                Interval best = tree.first();
                tree.remove(best);
                int place = best.toPlace;
                placeById[id] = place;
                used[place] = true;
                out.println(place);

                if (place + 1 <= best.to) {
                    Interval newInt = new Interval(place + 1, best.to);
                    starts[newInt.from] = newInt;
                    ends[newInt.to] = newInt;
                    tree.add(newInt);
                }

                if (place - 1 >= best.from) {
                    Interval newInt = new Interval(best.from, place - 1);
                    starts[newInt.from] = newInt;
                    ends[newInt.to] = newInt;
                    tree.add(newInt);
                }
            } else {
                int place = placeById[id];
                int from = place;
                used[place] = false;
                if (place != 1 && !used[place - 1]) {
                    Interval left = ends[place - 1];
                    tree.remove(left);
                    from = left.from;
                }
                int to = place;
                if (place != n && !used[place + 1]) {
                    Interval right = starts[place + 1];
                    tree.remove(right);
                    to = right.to;
                }

                Interval newInt = new Interval(from, to);
                starts[from] = newInt;
                ends[to] = newInt;
                tree.add(newInt);
            }
        }
    }

    @Override
    public void run() {
        in = new MyScanner();
        out = new PrintWriter(System.out);
        solve();
        in.close();
        out.close();
    }

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

    class Interval implements  Comparable<Interval> {
        public int from, to, dist, toPlace;

        Interval(int from, int to) {
            this.from = from;
            this.to = to;
            if (from == 1) {
                dist = to;
                toPlace = 1;
            } else if (to == n) {
                dist = n - from + 1;
                toPlace = n;
            } else {
                dist = (to - from + 2) >> 1;
                toPlace = from + dist - 1;
            }
        }

        @Override
        public int compareTo(Interval o) {
            if (dist != o.dist) {
                return o.dist - dist;
            }
            return from - o.from;
        }
    }

    /*
    END OF SOLUTION
     */

    public class MyScanner {
        private BufferedReader br;

        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        public MyScanner(String fileName) {
            try {
                br = new BufferedReader(new FileReader(fileName));
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
        }

        public void close() {
            try {
                br.close();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }

        private char read() {
            try {
                return (char) br.read();
            } catch (IOException e) {
                e.printStackTrace();
                return (char) -1;
            }
        }

        public char nextChar() {
            char c = read();
            while (Character.isWhitespace(c)) {
                c = read();
            }
            return c;
        }

        public String next() {
            StringBuilder sb = new StringBuilder();
            char c = read();
            while (Character.isWhitespace(c)) {
                c = read();
            }
            while (!Character.isWhitespace(c)) {
                sb.append(c);
                c = read();
            }
            return sb.toString();
        }

        public String nextLine() {
            try {
                return br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
                return null;
            }
        }

        private int digit(char c) {
            if (c >= '0' && c <= '9') {
                return c - '0';
            }
            return Character.toLowerCase(c) - 'a' + 10;
        }

        public int nextInt(int radix) {
            int ans = 0;
            char c = read();
            while (Character.isWhitespace(c)) {
                c = read();
            }
            boolean sign = false;
            if (c == '-') {
                sign = true;
                c = read();
            } else if (c == '+') {
                c = read();
            }
            while (!Character.isWhitespace(c)) {
                ans *= radix;
                ans += digit(c);
                c = read();
            }
            return sign ? (-ans) : ans;
        }

        public int nextInt() {
            return nextInt(10);
        }


        public long nextLong(int radix) {
            long ans = 0;
            char c = read();
            while (Character.isWhitespace(c)) {
                c = read();
            }
            boolean sign = false;
            if (c == '-') {
                sign = true;
                c = read();
            } else if (c == '+') {
                c = read();
            }
            while (!Character.isWhitespace(c)) {
                ans *= radix;
                ans += digit(c);
                c = read();
            }
            return sign ? (-ans) : ans;
        }

        public long nextLong() {
            return nextLong(10);
        }

        public int[] nextIntArray(int size, int radix) {
            int[] a = new int[size];
            for (int i = 0; i < size; ++i) {
                a[i] = nextInt(radix);
            }
            return a;
        }

        public int[] nextIntArray(int size) {
            return nextIntArray(size, 10);
        }

        public long[] nextLongArray(int size, int radix) {
            long[] a = new long[size];
            for (int i = 0; i < size; ++i) {
                a[i] = nextLong(radix);
            }
            return a;
        }

        public long[] nextLongArray(int size) {
            return nextLongArray(size, 10);
        }

        public char[][] nextWords(int lines) {
            char[][] a = new char[lines][];
            for (int i = 0; i < lines; ++i) {
                a[i] = next().toCharArray();
            }
            return a;
        }

        public int[][] nextIntArray2D(int n, int m, int radix) {
            int[][] a = new int[n][m];
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < m; ++j) {
                    a[i][j] = nextInt(radix);
                }
            }
            return a;
        }

        public int[][] nextIntArray2D(int n, int m) {
            return nextIntArray2D(n, m, 10);
        }

        public long[][] nextLongArray2D(int n, int m, int radix) {
            long[][] a = new long[n][m];
            for (int i = 0; i < n; ++i) {
                for (int j = 0; j < m; ++j) {
                    a[i][j] = nextLong(radix);
                }
            }
            return a;
        }

        public long[][] nextLongArray2D(int n, int m) {
            return nextLongArray2D(n, m, 10);
        }
    }
}