One day, at the "Russian Code Cup" event it was decided to play football as an out of competition event. All participants was divided into n teams and played several matches, two teams could not play against each other more than once.

The appointed Judge was the most experienced member — Pavel. But since he was the wisest of all, he soon got bored of the game and fell asleep. Waking up, he discovered that the tournament is over and the teams want to know the results of all the matches.

Pavel didn't want anyone to discover about him sleeping and not keeping an eye on the results, so he decided to recover the results of all games. To do this, he asked all the teams and learned that the real winner was friendship, that is, each team beat the other teams exactly k times. Help Pavel come up with chronology of the tournir that meets all the conditions, or otherwise report that there is no such table.

Input

The first line contains two integers — n and k (1 ≤ n, k ≤ 1000).

Output

In the first line print an integer m — number of the played games. The following m lines should contain the information about all the matches, one match per line. The i-th line should contain two integers ai and bi (1 ≤ ai, bi ≤ n; ai ≠ bi). The numbers ai and bi mean, that in the i-th match the team with number ai won against the team with number bi. You can assume, that the teams are numbered from 1 to n.

If a tournir that meets the conditions of the problem does not exist, then print -1.

Examples

Input

3 1


Output

3
1 2
2 3
3 1
/*Author: Satyajeet Singh, Delhi Technological University*/
import java.io.*;
import java.util.*;
import java.text.*; 
import java.lang.*;

public class Main {
/*********************************************Constants******************************************/
    static PrintWriter out=new PrintWriter(new OutputStreamWriter(System.out));        
    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static long mod=(long)1e9+7;
    static long mod1=998244353;
    static boolean sieve[];
    static ArrayList<Integer> primes;
    static ArrayList<Long> factorial;
    static HashSet<Integer> graph[];
/****************************************Solutions Begins***************************************************/
    public static void main (String[] args) throws Exception {
        String st[]=br.readLine().split(" ");
        int n=Integer.parseInt(st[0]);
        int k=Integer.parseInt(st[1]);
        Makegraph(n+1);
        ArrayList<Integer> list=new ArrayList<>();
        for(int i=1;i<=n;i++){
            for(int j=1;j<=n;j++){
                if(!graph[i].contains(j)&&!graph[j].contains(i)&&j!=i){
                addEdge(i,j);
                list.add(i);
                list.add(j);
                }
                if(graph[i].size()==k)break;
            }
        }
        boolean flag=true;
        for(int i=1;i<=n;i++){
            if(graph[i].size()!=k){
                flag=false;
                break;
            }
        }
        if(flag){
            out.println(list.size()/2);
            for(int i=0;i<list.size();i+=2){
                out.println(list.get(i)+" "+list.get(i+1));
            }
        }
        else{
            out.println(-1);
        }
/****************************************Solutions Ends*****************************************************/
        out.flush();
        out.close();
    }
/****************************************Template Begins***************************************************/
/***************************************Precision Printing************************************************/
    static void printPrecision(double d){
        DecimalFormat ft = new DecimalFormat("0.000000"); 
        out.println(ft.format(d));
    }
/******************************************Graph***********************************************************/
    static void Makegraph(int n){
        graph=new HashSet[n];
        for(int i=0;i<n;i++){
            graph[i]=new HashSet<>();
        }
    }
    static void addEdge(int a,int b){
        graph[a].add(b);
    }    
/*******************************************TRIPLET********************************************************/
    static class tripletComparator implements Comparator<triplet>{
        public int compare(triplet p1,triplet p2){
            if(p1.u<p2.u){
                return 1;
            }
            else if(p1.u>p2.u){
                return -1;
            }
            else{
                return 0;
            }
        }
    }
    static class triplet{
        int u;
        int v;
        int i;
        public triplet(int u,int v,int i){
            this.u=u;
            this.v=v;
            this.i=i;
        }
        public String toString() {
            return "[u=" + u + ", v=" + v + ", i="+i+"]";
        }
    }
/*********************************************PAIR**********************************************************/
    static class PairComp implements Comparator<Pair>{
        public int compare(Pair p1,Pair p2){
            if(p1.u>p2.u){
                return 1;
            }
            else if(p1.u<p2.u){
                return -1;
            }
            else{
                return p1.v-p2.v;
            }
        }
    }
    static class Pair implements Comparable<Pair> {
        int u;
        int v;
        int index=-1;
        public Pair(int u, int v) {
            this.u = u;
            this.v = v;
        }
 
        public int hashCode() {
            int hu = (int) (u ^ (u >>> 32));
            int hv = (int) (v ^ (v >>> 32));
            return 31 * hu + hv;
        }
 
        public boolean equals(Object o) {
            Pair other = (Pair) o;
            return u == other.u && v == other.v;
        }
 
        public int compareTo(Pair other) {
            if(index!=other.index)
                return Long.compare(index, other.index);
            return Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u);
        }
 
        public String toString() {
            return "[u=" + u + ", v=" + v + "]";
        }
    }
/*******************************************LONG PAIR******************************************************/
    static class PairCompL implements Comparator<Pairl>{
        public int compare(Pairl p1,Pairl p2){
            if(p1.u>p2.u){
                return 1;
            }
            else if(p1.u<p2.u){
                return -1;
            }
            else{
                return 0;
            }
        }
    }
    static class Pairl implements Comparable<Pair> {
            long u;
            long v;
            int index=-1;
            public Pairl(long u, long v) {
                this.u = u;
                this.v = v;
            }
    
            public int hashCode() {
                int hu = (int) (u ^ (u >>> 32));
                int hv = (int) (v ^ (v >>> 32));
                return 31 * hu + hv;
            }
    
            public boolean equals(Object o) {
                Pair other = (Pair) o;
                return u == other.u && v == other.v;
            }
    
            public int compareTo(Pair other) {
                if(index!=other.index)
                    return Long.compare(index, other.index);
                return Long.compare(v, other.v)!=0?Long.compare(v, other.v):Long.compare(u, other.u);
            }
    
            public String toString() {
                return "[u=" + u + ", v=" + v + "]";
            }
        }
/*****************************************DEBUG***********************************************************/
    public static void debug(Object... o) {
        System.out.println(Arrays.deepToString(o));
    }
/*****************************************NUMBER THEORY****************************************************/
/************************************MODULAR EXPONENTIATION***********************************************/
    static long modulo(long a,long b,long c) {
        long x=1;
        long y=a;
        while(b > 0){
            if(b%2 == 1){
                x=(x*y)%c;
            }
            y = (y*y)%c; // squaring the base
            b /= 2;
        }
        return  x%c;
    }
/********************************************GCD**********************************************************/
    static long gcd(long x, long y)
    {
        if(x==0)
            return y;
        if(y==0)
            return x;
        long r=0, a, b;
        a = (x > y) ? x : y; // a is greater number
        b = (x < y) ? x : y; // b is smaller number
        r = b;
        while(a % b != 0)
        {
            r = a % b;
            a = b;
            b = r;
        }
        return r;
    }
/******************************************SIEVE**********************************************************/
    static void sieveMake(int n){
        sieve=new boolean[n];
        Arrays.fill(sieve,true);
        sieve[0]=false;
        sieve[1]=false;
        for(int i=2;i*i<n;i++){
            if(sieve[i]){
                for(int j=i*i;j<n;j+=i){
                    sieve[j]=false;
                }
            }
        }
        primes=new ArrayList<Integer>();
        for(int i=0;i<n;i++){
            if(sieve[i]){
                primes.add(i);
            }
        }        
    }
/***************************************FACTORIAL*********************************************************/
    static void fact(int n){
        factorial=new ArrayList<>();
        factorial.add((long)1);
        for(int i=1;i<=n;i++){
            factorial.add((factorial.get(i-1)*i)%mod);
        }
    }
/*******************************************ncr*********************************************************/
    static long ncr(int n,int k){
        long aa=modulo(factorial.get(n-k),mod-2,mod);
        long bb=modulo(factorial.get(k),mod-2,mod);
        long cc=factorial.get(n);
        long ans=(aa*cc)%mod;
        ans=(ans*bb)%mod;
        return ans;
    }
/***************************************STRING REVERSE****************************************************/
    static String reverse(String str){
        char r[]=new char[str.length()];
        int j=0;
        for(int i=str.length()-1;i>=0;i--){
            r[j]=str.charAt(i);
            j++;
        }
        return new String(r);
    }
}
/********************************************End***********************************************************/