This morning Tolik has understood that while he was sleeping he had invented an incredible problem which will be a perfect fit for Codeforces! But, as a "Discuss tasks" project hasn't been born yet (in English, well), he decides to test a problem and asks his uncle.

After a long time thinking, Tolik's uncle hasn't any ideas on how to solve it. But, he doesn't want to tell Tolik about his inability to solve it, so he hasn't found anything better than asking you how to solve this task.

In this task you are given a cell field n ⋅ m, consisting of n rows and m columns, where point's coordinates (x, y) mean it is situated in the x-th row and y-th column, considering numeration from one (1 ≤ x ≤ n, 1 ≤ y ≤ m). Initially, you stand in the cell (1, 1). Every move you can jump from cell (x, y), which you stand in, by any non-zero vector (dx, dy), thus you will stand in the (x+dx, y+dy) cell. Obviously, you can't leave the field, but also there is one more important condition — you're not allowed to use one vector twice. Your task is to visit each cell of the field exactly once (the initial cell is considered as already visited).

Tolik's uncle is a very respectful person. Help him to solve this task!

Input

The first and only line contains two positive integers n, m (1 ≤ n ⋅ m ≤ 10^{6}) — the number of rows and columns of the field respectively.

Output

Print "-1" (without quotes) if it is impossible to visit every cell exactly once.

Else print n ⋅ m pairs of integers, i-th from them should contain two integers x_i, y_i (1 ≤ x_i ≤ n, 1 ≤ y_i ≤ m) — cells of the field in order of visiting, so that all of them are distinct and vectors of jumps between them are distinct too.

Notice that the first cell should have (1, 1) coordinates, according to the statement.

Examples

Input


2 3


Output


1 1
1 3
1 2
2 2
2 3
2 1

Input


1 1


Output


1 1

Note

The vectors from the first example in the order of making jumps are (0, 2), (0, -1), (1, 0), (0, 1), (0, -2).
import java.io.*;
import java.math.BigDecimal;
import java.util.*;
import java.util.Map.Entry;
public class Contest1 {
    ////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////                                                                                                               /////////
////////                                                                                                               /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMMMM      MMMMMM      OOO      OOO        SSSS   SSS     EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEE           MMMM MMM  MMM MMMM    OOO          OOO    SSSS       SSS   EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM  MMMMMM  MMMM   OOO            OOO   SSSS             EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM  OOO              OOO   SSSSSSS         EEEEE          /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO      SSSSSS       EEEEEEEEEEE    /////////
////////   HHHHHHHHHHHHHHHH  EEEEEEEEEEE     MMMM          MMMM  OOO              OOO         SSSSSSS   EEEEEEEEEEE    /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM   OOO            OOO              SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEE           MMMM          MMMM    OOO          OOO     SSS       SSSS  EEEEE          /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM      OOO      OOO        SSS    SSSS    EEEEEEEEEEEEE  /////////
////////   HHHH        HHHH  EEEEEEEEEEEEE   MMMM          MMMM         OOOOOO             SSSSSSS      EEEEEEEEEEEEE  /////////
////////                                                                                                               /////////
////////                                                                                                               /////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

    public static void main(String[] args) throws IOException, InterruptedException {
        Scanner sc = new Scanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = sc.nextInt();
        int m = sc.nextInt();
        int currow=1;
        int curcol=1;
        StringBuilder sol = new StringBuilder();

        while (true){
            if (currow>n/2)break;
            sol.append(currow+" "+curcol+"\n");
            sol.append((n-currow+1)+" "+(m-curcol+1)+"\n");
            curcol++;
            if (curcol>m){
                curcol=1;
                currow++;
            }
        }
        if (n%2==1){
            while (true) {
                sol.append(currow + " " + curcol + "\n");
                if (curcol>m/2||curcol==(m-curcol+1))break;
                sol.append(currow + " " + (m - curcol + 1) + "\n");
                curcol++;
                if (curcol>(m+1)/2)break;
            }
        }
        pw.println(sol);
        pw.flush();
    }
    static class Pair{
        int a,b;
        Pair(int x,int y){
            a=x;
            b=y;
        }
    }
    static class UnionFind {
        int[] p, rank, setSize;
        int numSets;

        public UnionFind(int N)
        {
            p = new int[numSets = N];
            rank = new int[N];
            setSize = new int[N];
            for (int i = 0; i < N; i++) {  p[i] = i; setSize[i] = 1; }
        }

        public int findSet(int i) { return p[i] == i ? i : (p[i] = findSet(p[i])); }

        public boolean isSameSet(int i, int j) { return findSet(i) == findSet(j); }

        public void unionSet(int i, int j)
        {
            if (isSameSet(i, j))
                return;
            numSets--;
            int x = findSet(i), y = findSet(j);
            if(rank[x] > rank[y]) { p[y] = x; setSize[x] += setSize[y]; }
            else
            {	p[x] = y; setSize[y] += setSize[x];
                if(rank[x] == rank[y]) rank[y]++;
            }
        }

        public int numDisjointSets() { return numSets; }

        public int sizeOfSet(int i) { return setSize[findSet(i)]; }
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(FileReader r) {
            br = new BufferedReader(r);
        }

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }

}