Problem: The king of Berland organizes a ball! n pair are invited to the ball, they are numbered from 1 to n. Each pair consists of one man and one woman. Each dancer (either man or woman) has a monochrome costume. The color of each costume is represented by an integer from 1 to k, inclusive.

Let b_i be the color of the man's costume and g_i be the color of the woman's costume in the i-th pair. You have to choose a color for each dancer's costume (i.e. values b_1, b_2, ..., b_n and g_1, g_2, ... g_n) in such a way that:

  1. for every i: b_i and g_i are integers between 1 and k, inclusive; 
  2. there are no two completely identical pairs, i.e. no two indices i, j (i ≠ j) such that b_i = b_j and g_i = g_j at the same time; 
  3. there is no pair such that the color of the man's costume is the same as the color of the woman's costume in this pair, i.e. b_i ≠ g_i for every i; 
  4. for each two consecutive (adjacent) pairs both man's costume colors and woman's costume colors differ, i.e. for every i from 1 to n-1 the conditions b_i ≠ b_{i + 1} and g_i ≠ g_{i + 1} hold. 



Let's take a look at the examples of bad and good color choosing (for n=4 and k=3, man is the first in a pair and woman is the second):

Bad color choosing: 

  * (1, 2), (2, 3), (3, 2), (1, 2) — contradiction with the second rule (there are equal pairs); 
  * (2, 3), (1, 1), (3, 2), (1, 3) — contradiction with the third rule (there is a pair with costumes of the same color); 
  * (1, 2), (2, 3), (1, 3), (2, 1) — contradiction with the fourth rule (there are two consecutive pairs such that colors of costumes of men/women are the same). 



Good color choosing: 

  * (1, 2), (2, 1), (1, 3), (3, 1); 
  * (1, 2), (3, 1), (2, 3), (3, 2); 
  * (3, 1), (1, 2), (2, 3), (3, 2). 



You have to find any suitable color choosing or say that no suitable choosing exists.

Input

The only line of the input contains two integers n and k (2 ≤ n, k ≤ 2 ⋅ 10^5) — the number of pairs and the number of colors.

Output

If it is impossible to find any suitable colors choosing, print "NO".

Otherwise print "YES" and then the colors of the costumes of pairs in the next n lines. The i-th line should contain two integers b_i and g_i — colors of costumes of man and woman in the i-th pair, respectively.

You can print each letter in any case (upper or lower). For example, "YeS", "no" and "yES" are all acceptable.

Examples

Input


4 3


Output


YES
3 1
1 3
3 2
2 3


Input


10 4


Output


YES
2 1
1 3
4 2
3 4
4 3
3 2
2 4
4 1
1 4
3 1


Input


13 4


Output


NO

Solution (in JAVA):

Solution:
import javax.print.attribute.standard.PrinterMessageFromOperator;
import java.io.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;
public class Main {
    public static void main(String[] args) throws Exception {
        new Main().run();}

//    int[] h,ne,to,wt;
//    int ct = 0;
//    int n;
//    void graph(int n,int m){
//        h = new int[n];
//        Arrays.fill(h,-1);
////        sccno = new int[n];
////        dfn = new int[n];
////        low = new int[n];
////        iscut = new boolean[n];
//        ne = new int[2*m];
//        to = new int[2*m];
//        wt = new int[2*m];
//        ct = 0;
//    }
//    void add(int u,int v,int w){
//        to[ct] = v;
//        ne[ct] = h[u];
//        wt[ct] = w;
//        h[u] = ct++;
//    }
//
//    int color[],dfn[],low[],stack[] = new int[1000000],cnt[];
//    int sccno[];
//    boolean iscut[];
//    int time = 0,top = 0;
//    int scc_cnt = 0;
//
//    // 有向图的强连通分量
//    void tarjan(int u) {
//        low[u] = dfn[u]= ++time;
//        stack[top++] = u;
//        for(int i=h[u];i!=-1;i=ne[i]) {
//            int v = to[i];
//            if(dfn[v]==0) {
//                tarjan(v);
//                low[u]=Math.min(low[u],low[v]);
//            } else if(sccno[v]==0) {
//                // dfn>0 but sccno==0, means it's in current stack
//                low[u]=Math.min(low[u],low[v]);
//            }
//        }
//
//        if(dfn[u]==low[u]) {
//            sccno[u] = ++scc_cnt;
//            while(stack[top-1]!=u) {
//                sccno[stack[top-1]] = scc_cnt;
//                --top;
//            }
//            --top;
//        }
//    }
//
//    //缩点, topology sort
//    int[] h1,to1,ne1;
//    int ct1 = 0;
//    void point(){
//        for(int i=0;i<n;i++) {
//            if(dfn[i]==0) tarjan(i);//有可能图不连通，所以要循环判断。
//        }
//        // 入度
//        int du[] = new int[scc_cnt+1];
//        h1 = new int[scc_cnt+1];
//        Arrays.fill(h1, -1);
//        to1 = new int[scc_cnt*scc_cnt];
//        ne1 = new int[scc_cnt*scc_cnt];
//        // scc_cnt 个点
//
//        for(int i=1;i<=n;i++) {
//            for(int j=h[i]; j!=-1; j=ne[j]) {
//                int y = to[j];
//                if(sccno[i] != sccno[y]) {
//                    // add(sccno[i],sccno[y]);  // 建新图
//                    to1[ct1] = sccno[y];
//                    ne1[ct1] = h[sccno[i]];
//                    h[sccno[i]] = ct1++;
//                    du[sccno[y]]++; //存入度
//                }
//            }
//        }
//
//        int q[] = new int[100000];
//        int end = 0;
//        int st = 0;
//        for(int i=1;i<=scc_cnt;++i){
//            if(du[i]==0){
//                q[end++] = i;
//            }
//        }
//
//        int dp[] = new int[scc_cnt+1];
//        while(st<end){
//            int cur = q[st++];
//            for(int i=h1[cur];i!=-1;i=ne1[i]){
//                int y = to[i];
//                // dp[y] += dp[cur];
//                if(--du[y]==0){
//                    q[end++] = y;
//                }
//            }
//        }
//    }
//
//
//
//
//    int fa[];
//    int faw[];
//
//    int dep = -1;
//    int pt = 0;
//    void go(int rt,int f,int dd){
//
//        int p = 0;
//        stk[p] = rt;
//        lk[p] = 0;
//        fk[p] = f;p++;
//        while(p>0) {
//            int cur = stk[p - 1];
//            int fp = fk[p - 1];
//            int ll = lk[p - 1];
//            p--;
//
//
//            if (ll > dep) {
//                dep = ll;
//                pt = cur;
//            }
//            for (int i = h[cur]; i != -1; i = ne[i]) {
//                int v = to[i];
//                if (fp == v) continue;
//
//                stk[p] = v;
//                lk[p] = ll + wt[i];
//                fk[p] = cur;
//                p++;
//            }
//        }
//    }
//    int pt1 = -1;
//    void go1(int rt,int f,int dd){
//
//        int p = 0;
//        stk[p] = rt;
//        lk[p] = 0;
//        fk[p] = f;p++;
//        while(p>0) {
//            int cur = stk[p - 1];
//            int fp = fk[p - 1];
//            int ll = lk[p - 1];
//            p--;
//
//
//            if (ll > dep) {
//                dep = ll;
//                pt1 = cur;
//            }
//
//            fa[cur] = fp;
//            for (int i = h[cur]; i != -1; i = ne[i]) {
//                int v = to[i];
//                if (v == fp) continue;
//                faw[v] = wt[i];
//                stk[p] = v;
//                lk[p] = ll + wt[i];
//                fk[p] = cur;
//                p++;
//            }
//        }
//    }
//
//    int r = 0;
//    int stk[] = new int[301];
//    int fk[] = new int[301];
//    int lk[] = new int[301];
//    void ddfs(int rt,int t1,int t2,int t3,int l){
//
//
//        int p = 0;
//        stk[p] = rt;
//        lk[p] = 0;
//        fk[p] = t3;p++;
//        while(p>0){
//            int cur = stk[p-1];
//            int fp = fk[p-1];
//            int ll = lk[p-1];
//            p--;
//            r = Math.max(r,ll);
//            for(int i=h[cur];i!=-1;i=ne[i]){
//                int v = to[i];
//                if(v==t1||v==t2||v==fp) continue;
//                stk[p] = v;
//                lk[p] = ll+wt[i];
//                fk[p] = cur;p++;
//            }
//        }
//
//
//
//    }


    static long mul(long a, long b, long p)
    {
        long res=0,base=a;
        while(b>0)
        {
            if((b&1L)>0)
                res=(res+base)%p;
            base=(base+base)%p;
            b>>=1;
        }
        return res;
    }

    static long mod_pow(long k,long n,long p){
        long res = 1L;
        long temp = k;
        while(n!=0L){
            if((n&1L)==1L){
                res = (res*temp)%p;
            }
            temp = (temp*temp)%p;
            n = n>>1L;
        }
        return res%p;
    }
    int ct = 0;
    int f[]  =new int[200001];
    int b[]  =new int[200001];
    int str[]  =new int[200001];

    void go(int rt,List<Integer> g[]){
        str[ct] = rt;
        f[rt] = ct;
        for(int cd:g[rt]){
            ct++;
            go(cd,g);
        }
        b[rt] = ct;
    }
    int add =0;

    void sort(long a[]) {
        Random rd = new Random();
        for (int i = 1; i < a.length; ++i) {
            int p = rd.nextInt(i); long x = a[p]; a[p] = a[i]; a[i] = x;
        }
        Arrays.sort(a);
    }

    void dfs(int from,int k){

    }


    void solve() {

       long n = nl();
       long k = nl();
       long c = k*k-k;
       if(c<n){
           println("NO");return;
       }
            long nn = n;
           println("YES");
           for(int from =1; from <=k ;++from) {
               for (int i = from + 1; i <= k; ++i) {
                   if(nn>0) {
                       println(from + " " + i);--nn;
                   }else{
                       return;
                   }
                   if(nn>0) {
                       println(i + " " + from);
                       --nn;
                   }else{
                       return;
                   }
               }
           }
           return;










        //N , M , K , a , b , c , d . 其中N , M是矩阵的行列数；K 是上锁的房间数目，(a, b)是起始位置，(c, d)是出口位置


//        int n = ni();
//        int m = ni();
//        int k = ni();
//        int a = ni();
//        int b = ni();
//        int c = ni();
//        int d = ni();
//
//
//        char cc[][] = nm(n,m);
//        char keys[][] = new char[n][m];
//
//        char ky = 'a';
//        for(int i=0;i<k;++i){
//            int x = ni();
//            int y = ni();
//            keys[x][y] = ky;
//            ky++;
//        }
//        int f1[] = {a,b,0};
//
//        int dd[][] = {{0,1},{0,-1},{1,0},{-1,0}};
//
//        Queue<int[]> q =  new LinkedList<>();
//        q.offer(f1);
//        int ts = 1;
//
//        boolean vis[][][] = new boolean[n][m][33];
//
//        while(q.size()>0){
//            int sz = q.size();
//            while(sz-->0) {
//                int cur[] = q.poll();
//                vis[cur[0]][cur[1]][cur[2]] = true;
//
//                int x = cur[0];
//                int y = cur[1];
//
//                for (int u[] : dd) {
//                       int lx = x +  u[0];
//                       int ly = y +  u[1];
//                       if (lx >= 0 && ly >= 0 && lx < n && ly < m && (cc[lx][ly] != '#')&&!vis[lx][ly][cur[2]]){
//                            char ck =cc[lx][ly];
//                            if(ck=='.'){
//                                if(lx==c&&ly==d){
//                                    println(ts); return;
//                                }
//                                if(keys[lx][ly]>='a'&&keys[lx][ly]<='z') {
//                                    int cao = cur[2] | (1 << (keys[lx][ly] - 'a'));
//                                    q.offer(new int[]{lx, ly, cao});
//                                    vis[lx][ly][cao] = true;
//                                }else {
//
//                                    q.offer(new int[]{lx, ly, cur[2]});
//                                }
//
//                            }else if(ck>='A'&&ck<='Z'){
//                                int g = 1<<(ck-'A');
//                                if((g&cur[2])>0){
//                                    if(lx==c&&ly==d){
//                                        println(ts); return;
//                                    }
//                                    if(keys[lx][ly]>='a'&&keys[lx][ly]<='z') {
//
//                                        int cao = cur[2] | (1 << (keys[lx][ly] - 'a'));
//                                        q.offer(new int[]{lx, ly, cao});
//                                        vis[lx][ly][cao] = true;;
//                                    }else {
//
//                                        q.offer(new int[]{lx, ly, cur[2]});
//                                    }
//                                }
//                            }
//                       }
//                }
//
//                }
//            ts++;
//        }
//        println(-1);




//        int n = ni();
//
//        HashSet<String> st = new HashSet<>();
//        HashMap<String,Integer> mp = new HashMap<>();
//
//
//        for(int i=0;i<n;++i){
//            String s  = ns();
//            int id= 1;
//            if(mp.containsKey(s)){
//                int u = mp.get(s);
//                id = u;
//
//            }
//
//            if(st.contains(s)) {
//
//                while (true) {
//                    String ts = s + id;
//                    if (!st.contains(ts)) {
//                        s = ts;
//                        break;
//                    }
//                    id++;
//                }
//                mp.put(s,id+1);
//            }else{
//                mp.put(s,1);
//            }
//            println(s);
//            st.add(s);
//
//        }

//        int t = ni();
//
//        for(int i=0;i<t;++i){
//            int n = ni();
//            long w[] = nal(n);
//
//            Map<Long,Long> mp = new HashMap<>();
//            PriorityQueue<long[]> q =new PriorityQueue<>((xx,xy)->{return Long.compare(xx[0],xy[0]);});
//
//            for(int j=0;j<n;++j){
//                q.offer(new long[]{w[j],0});
//                mp.put(w[j],mp.getOrDefault(w[j],0L)+1L);
//            }
//
//            while(q.size()>=2){
//                long f[] = q.poll();
//                long y1 = f[1];
//                if(y1==0){
//                    y1 = mp.get(f[0]);
//                    if(y1==1){
//                        mp.remove(f[0]);
//                    }else{
//                        mp.put(f[0],y1-1);
//                    }
//                }
//                long g[] = q.poll();
//                long y2 = g[1];
//                if(y2==0){
//                    y2 = mp.get(g[0]);
//                    if(y2==1){
//                        mp.remove(g[0]);
//                    }else{
//                        mp.put(g[0],y2-1);
//                    }
//                }
//                q.offer(new long[]{f[0]+g[0],2L*y1*y2});
//
//            }
//            long r[] = q.poll();
//            println(r[1]);
//
//
//
//
//        }
        //  int o= 9*8*7*6;
        //  println(o);


//       int t = ni();
//       for(int i=0;i<t;++i){
//           long a = nl();
//           int k  = ni();
//           if(k==1){
//               println(a);
//               continue;
//           }
//
//           int f = (int)(a%10L);
//           int s = 1;
//           int j = 0;
//           for(;j<30;j+=2){
//               int u = f-j;
//               if(u<0){
//                   u = 10+u;
//               }
//               s = u*s;
//               s = s%10;
//               if(s==k){
//                   break;
//               }
//           }
//
//           if(s==k) {
//               println(a - j - 2);
//           }else{
//               println(-1);
//           }
//
//
//
//
//       }

//     int m = ni();
//     h = new int[n];
//     to = new int[2*(n-1)];
//     ne = new int[2*(n-1)];
//     wt = new int[2*(n-1)];
//
//     for(int i=0;i<n-1;++i){
//         int u = ni()-1;
//         int v = ni()-1;
//
//     }
        //  long a[] = nal(n);


//        int n = ni();
//        int k = ni();
//        t1 = new long[200002];
//
//        int p[][] = new int[n][3];
//
//        for(int i=0;i<n;++i){
//            p[i][0]  = ni();
//            p[i][1]  = ni();
//            p[i][2]  = i+1;
//        }
//        Arrays.sort(p, new Comparator<int[]>() {
//            @Override
//            public int compare(int[] x, int[] y) {
//                if(x[1]!=y[1]){
//                    return Integer.compare(x[1],y[1]);
//                }
//                return Integer.compare(y[0], x[0]);
//            }
//        });
//
//        for(int i=0;i<n;++i){
//            int ck = p[i][0];
//
//        }

















    }









//    int []h,to,ne,wt;

    long t1[];
    //    long t2[];
    void update(long[] t,int i,long v){
        for(;i<t.length;i+=(i&-i)){
            t[i] += v;
        }
    }
    long get(long[] t,int i){
        long s = 0;
        for(;i>0;i-=(i&-i)){
            s += t[i];
        }
        return s;
    }

    int equal_bigger(long t[],long v){
        int s=0,p=0;
        for(int i=Integer.numberOfTrailingZeros(Integer.highestOneBit(t.length));i>=0;--i) {
            if(p+(1<<i)< t.length && s + t[p+(1<<i)] < v){
                v -= t[p+(1<<i)];
                p |= 1<<i;
            }
        }
        return p+1;
    }









    static class S{
        int l = 0;
        int r = 0 ;
        long le = 0;
        long ri = 0;
        long tot = 0;
        long all = 0;

        public S(int l,int r) {
            this.l = l;
            this.r = r;
        }
    }

    static S a[];
    static int[] o;

    static void init(int[] f){
        o = f;
        int len = o.length;
        a = new S[len*4];
        build(1,0,len-1);
    }

    static void build(int num,int l,int r){
        S cur = new S(l,r);
        if(l==r){
            a[num] = cur;
            return;
        }else{
            int m = (l+r)>>1;
            int le = num<<1;
            int ri = le|1;
            build(le, l,m);
            build(ri, m+1,r);
            a[num] = cur;
            pushup(num, le, ri);
        }
    }



    //    static int query(int num,int l,int r){
//
//        if(a[num].l>=l&&a[num].r<=r){
//            return a[num].tot;
//        }else{
//            int m = (a[num].l+a[num].r)>>1;
//            int le = num<<1;
//            int ri = le|1;
//            pushdown(num, le, ri);
//            int ma = 1;
//            int mi = 100000001;
//            if(l<=m) {
//                int r1 = query(le, l, r);
//                ma = ma*r1;
//
//            }
//            if(r>m){
//                int r2 = query(ri, l, r);
//                ma = ma*r2;
//            }
//            return ma;
//        }
//    }
    static long dd = 10007;
    static void update(int num,int l,long v){
        if(a[num].l==a[num].r){
            a[num].le = v%dd;
            a[num].ri = v%dd;
            a[num].all = v%dd;
            a[num].tot = v%dd;
        }else{
            int m = (a[num].l+a[num].r)>>1;
            int le = num<<1;
            int ri = le|1;
            pushdown(num, le, ri);
            if(l<=m){
                update(le,l,v);
            }
            if(l>m){
                update(ri,l,v);
            }
            pushup(num,le,ri);
        }
    }

    static void pushup(int num,int le,int ri){
        a[num].all = (a[le].all*a[ri].all)%dd;
        a[num].le = (a[le].le + a[le].all*a[ri].le)%dd;
        a[num].ri = (a[ri].ri + a[ri].all*a[le].ri)%dd;
        a[num].tot = (a[le].tot + a[ri].tot + a[le].ri*a[ri].le)%dd;


        //a[num].res[1] = Math.min(a[le].res[1],a[ri].res[1]);
    }
    static void pushdown(int num,int le,int ri){

    }


    int gcd(int a,int b){ return b==0?a: gcd(b,a%b);}
    InputStream is;PrintWriter out;
    void run() throws Exception {is = System.in;out = new PrintWriter(System.out);solve();out.flush();}
    private byte[] inbuf = new byte[2];
    public int lenbuf = 0, ptrbuf = 0;
    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {lenbuf = is.read(inbuf);} catch (IOException e) {throw new InputMismatchException();}
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];}
    private boolean isSpaceChar(int c) {return !(c >= 33 && c <= 126);}
    private int skip() {int b;while((b = readByte()) != -1 && isSpaceChar(b));return b;}
    private double nd() {return Double.parseDouble(ns());}
    private char nc() {return (char) skip();}
    private char ncc() {int b;while((b = readByte()) != -1 && !(b >= 32 && b <= 126));return (char)b;}
    private String ns() {int b = skip();StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);b = readByte(); }
        return sb.toString();}
    private char[] ns(int n) {char[] buf = new char[n];int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) { buf[p++] = (char) b;b = readByte(); }
        return n == p ? buf : Arrays.copyOf(buf, p);}
    private String nline() {int b = skip();StringBuilder sb = new StringBuilder();
        while (!isSpaceChar(b) || b == ' ') { sb.appendCodePoint(b);b = readByte(); }
        return sb.toString();}
    private char[][] nm(int n, int m) {char[][] a = new char[n][];for (int i = 0; i < n; i++) a[i] = ns(m);return a;}
    private int[] na(int n) {int[] a = new int[n];for (int i = 0; i < n; i++) a[i] = ni();return a;}
    private long[] nal(int n) { long[] a = new long[n];for (int i = 0; i < n; i++) a[i] = nl();return a;}
    private int ni() { int num = 0, b; boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')){};
        if (b == '-') { minus = true; b = readByte(); }
        while (true) {
            if (b >= '0' && b <= '9') num = (num << 3) + (num << 1) + (b - '0');
            else return minus ? -num : num;
            b = readByte();}}
    private long nl() { long num = 0; int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')){};
        if (b == '-') { minus = true; b = readByte(); }
        while (true) {
            if (b >= '0' && b <= '9')  num = num * 10 + (b - '0');
            else return minus ? -num : num;
            b = readByte();}}
    void print(Object obj){out.print(obj);}
    void println(Object obj){out.println(obj);}
    void println(){out.println();}
}