Problem: You are given two integers b and w. You have a chessboard of size 10^9 × 10^9 with the top left cell at (1; 1), the cell (1; 1) is painted white.

Your task is to find a connected component on this chessboard that contains exactly b black cells and exactly w white cells. Two cells are called connected if they share a side (i.e. for the cell (x, y) there are at most four connected cells: (x - 1, y), (x + 1, y), (x, y - 1), (x, y + 1)). A set of cells is called a connected component if for every pair of cells C_1 and C_2 from this set, there exists a sequence of cells c_1, c_2, ..., c_k such that c_1 = C_1, c_k = C_2, all c_i from 1 to k are belong to this set of cells and for every i ∈ [1, k - 1], cells c_i and c_{i + 1} are connected.

Obviously, it can be impossible to find such component. In this case print "NO". Otherwise, print "YES" and any suitable connected component.

You have to answer q independent queries.

Input

The first line of the input contains one integer q (1 ≤ q ≤ 10^5) — the number of queries. Then q queries follow.

The only line of the query contains two integers b and w (1 ≤ b, w ≤ 10^5) — the number of black cells required and the number of white cells required.

It is guaranteed that the sum of numbers of cells does not exceed 2 ⋅ 10^5 (∑ w + ∑ b ≤ 2 ⋅ 10^5).

Output

For each query, print the answer to it.

If it is impossible to find the required component, print "NO" on the first line.

Otherwise, print "YES" on the first line. In the next b + w lines print coordinates of cells of your component in any order. There should be exactly b black cells and w white cells in your answer. The printed component should be connected.

If there are several answers, you can print any. All coordinates in the answer should be in the range [1; 10^9].

Example

Input


3
1 1
1 4
2 5


Output


YES
2 2
1 2
YES
2 3
1 3
3 3
2 2
2 4
YES
2 3
2 4
2 5
1 3
1 5
3 3
3 5

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
public final class code
// class code
// public class Solution
{
    static void solve()throws IOException
    {
        int b=nextInt();
        int w=nextInt();
        boolean flag=false;
        if(w>b)
        {
            int temp=w;
            w=b;
            b=temp;
            flag=true;
        }
        ArrayList<Pair> list=new ArrayList<>();
        int x=2,y=2;
        for(int i=1;i<=w;i++)
        {
            list.add(new Pair(x,y));
            y+=2;
        }
        int n=list.size();
        for(int i=0;i<n;i++)
        {
            Pair p=list.get(i);
            list.add(new Pair(p.first,p.second+1));
            b--;
        }
        
        for(int i=0;i<n && b-->0;i++)
        {
            Pair p=list.get(i);
            list.add(new Pair(p.first-1,p.second));
        }
        for(int i=0;i<n && b-->0;i++)
        {
            Pair p=list.get(i);
            list.add(new Pair(p.first+1,p.second));
        }
        if(b>0)
        {
            list.add(new Pair(2,1));
            b--;
        }
        // debug(list);
        if(b>0)
            out.println("NO");
        else
        {
            out.println("YES");
            for(Pair i:list)
                out.println(i.first+" "+(flag?i.second+1:i.second));
        }
    }


    
     
    ///////////////////////////////////////////////////////////
    public static void main(String args[])throws IOException
    {
        br=new BufferedReader(new InputStreamReader(System.in));
        out=new PrintWriter(new BufferedOutputStream(System.out));
        random=new Random();
         
        // solve();
         
        int t=nextInt();
        for(int i=1;i<=t;i++)
        {
           // out.print("Case #"+i+": ");
            solve();
        }
         
        out.close();
    }
     
    static final long mod=(int)(1e9+7);
    static final int inf=(int)(1e9+1);
    // static final long inf=(long)(1e18);
     
    static class Pair implements Comparable<Pair>
    {
        int first,second;
        Pair(int a,int b)
        {
            first=a;
            second=b;
        }
        public int compareTo(Pair p)
        {
            return first-p.first;
        }
        public String toString()
        {
            return first+" "+second;
        }
    }
    static class Triplet
    {
        int first,second,third;
        Triplet(int a,int b,int c)
        {
            first=a;
            second=b;
            third=c;
        }
    }
    
    static long modinv(long x)
    {
        return modpow(x,mod-2);
    }
    static long modpow(long a,long b)
    {
        if(b==0)
            return 1;
        long x=modpow(a,b/2);
        x=(x*x)%mod;
        if(b%2==1)
            return (x*a)%mod;
        return x;
    } 
    static int max(int ... a)
    {
    int ret=a[0];
    for(int i=1;i<a.length;i++)
    ret=Math.max(ret,a[i]);
    return ret;
    }
    static int min(int ... a)
    {
    int ret=a[0];
    for(int i=1;i<a.length;i++)
    ret=Math.min(ret,a[i]);
    return ret;
    }
    static void debug(Object ... a)
    {
    System.out.print("> ");
    for(int i=0;i<a.length;i++)
    System.out.print(a[i]+" ");
    System.out.println();
    }
    static void debug(int a[]){debuga(Arrays.stream(a).boxed().toArray());}
    static void debug(long a[]){debuga(Arrays.stream(a).boxed().toArray());}
    static void debuga(Object a[])
    {
    System.out.print("> ");
    for(int i=0;i<a.length;i++)
    System.out.print(a[i]+" ");
    System.out.println();
    }
    static Random random;
    static BufferedReader br;
    static StringTokenizer st;
    static PrintWriter out;
    static String nextToken()throws IOException
    {
    while(st==null || !st.hasMoreTokens())
    st=new StringTokenizer(br.readLine());
    return st.nextToken();
    }
    static String nextLine()throws IOException
    {
    return br.readLine();
    }
    static int nextInt()throws IOException
    {
    return Integer.parseInt(nextToken());
    }
    static long nextLong()throws IOException
    {
    return Long.parseLong(nextToken());
    }
    static double nextDouble()throws IOException
    {
    return Double.parseDouble(nextToken());
    }
}