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.BufferedReader; 
import java.io.IOException; 
import java.io.InputStreamReader; 
import java.util.*; 
import java.util.StringTokenizer; 
import java.io.PrintWriter;
import java.io.*;

import java.util.stream.Collectors.*;
import java.lang.*;
import static java.util.stream.Collectors.*;
import static java.util.Map.Entry.*;
public class Ideo
{ 
    static class FastReader 
    { 
        BufferedReader br; 
        StringTokenizer st; 
  
        public FastReader() 
        { 
            br = new BufferedReader(new
                     InputStreamReader(System.in)); 
        } 
  
        String next() 
        { 
            while (st == null || !st.hasMoreElements()) 
            { 
                try
                { 
                    st = new StringTokenizer(br.readLine()); 
                } 
                catch (IOException  e) 
                { 
                    e.printStackTrace(); 
                } 
            } 
            return st.nextToken(); 
        } 
  
        int nextInt() 
        { 
            return Integer.parseInt(next()); 
        } 
  
        long nextLong() 
        { 
            return Long.parseLong(next()); 
        } 
  
        double nextDouble() 
        { 
            return Double.parseDouble(next()); 
        } 
  
        String nextLine() 
        { 
            String str = ""; 
            try
            { 
                str = br.readLine(); 
            } 
            catch (IOException e) 
            { 
                e.printStackTrace(); 
            } 
            return str; 
        } 
    }
   
static class aksh
{
    
    int x;
    int y;
    int moves;

    public aksh(int a,int b,int c) 
    {
        x = a;
        y = b;
        moves=c;
    }
}
static int power(int x,int y) 
{ 
    int res = 1;      // Initialize result 
  
      // Update x if it is more than or  
                // equal to p 
  
    while (y > 0) 
    { 
        // If y is odd, multiply x with result 
        if (y%2==1) 
            res = (res*x); 
  
        // y must be even now 
        y = y>>1; // y = y/2 
        x = (x*x);   
    } 
    return res; 
} 
 
 static int gcd(int a, int b) 
    { 
        if (a == 0) 
            return b; 
        return gcd(b % a, a); 
    } 


  static boolean compareSeq(char[] S, int x, int y, int n) 
    { 
        for (int i = 0; i < n; i++)
         {

            if (S[x] < S[y]) 
               return true;
            else if (S[x] > S[y]) 
                return false; 
            x = (x + 1) % n; 
            y = (y + 1) % n; 
        } 
        return true; 
    } 

    static void build(long[] sum,int[] arr,int n)
    {
      for(int i=0;i<(1<<n);i++)
      {
        long total=0;
        for(int j=0;j<n;j++)
        {
          if((i & (1 << j)) > 0)
            total+=arr[j];
        }

        sum[i]=total;
      }
    }

 
     static int count(long arr[], long x, int n) 
       {

        int l=0;
        int h=n-1;

        int res=-1;
        int mid=-1;
        while(l<=h)
        {
          mid=l+(h-l)/2;
          if(x==arr[mid])
          {
            res=mid;
            h=mid-1;
          }
          else if(x<arr[mid])
            h=mid-1;
          else
            l=mid+1;
        }

        if(res==-1)
          return 0;

        //res is first index and res1 is last index of an element in a sorted array total number of occurences is (res1-res+1)

        int res1=-1;
        l=0;
        h=n-1;
        while(l<=h)
        {
          mid=l+(h-l)/2;
          if(x==arr[mid])
          {
            res1=mid;
            l=mid+1;
          }
          else if(x<arr[mid])
            h=mid-1;
          else
            l=mid+1;
        }



        if(res1==-1)
          return 0;
        if(res!=-1 && res1!=-1)
          return (res1-res+1);

        return 0;

       } 

       static int parity(int a)
       {
    a^=a>>16;
    a^=a>>8;
    a^=a>>4;
    a^=a>>2;
    a^=a>>1;
    return a&1;
  }
/*
  PriorityQueue<aksh> pq = new PriorityQueue<>((o1, o2) -> {
            if (o1.p < o2.p)
                return 1;
            else if (o1.p > o2.p)
                return -1;
            else
                return 0;

        });//decreasing order acc to p*/
static int power(int x, int y, int m)  
    { 
        if (y == 0) 
            return 1; 
          
        int p = power(x, y / 2, m) % m; 
        p = (p * p) % m; 
      
        if (y % 2 == 0) 
            return p; 
        else
            return (x * p) % m; 
    } 
static int modinv(int a, int m) 
    { 
        int g = gcd(a, m); 
        if (g != 1) 
            return 0;
        else 
        { 
           return power(a, m - 2, m); 
        } 
        //return 0;
    } 

static int[] product(int[] nums) {
    int[] result = new int[nums.length];
 
    int[] t1 = new int[nums.length];
    int[] t2 = new int[nums.length];
 
    t1[0]=1;
    t2[nums.length-1]=1;
 
    //scan from left to right
    for(int i=0; i<nums.length-1; i++){
        t1[i+1] = nums[i] * t1[i];
    }
 
    //scan from right to left
    for(int i=nums.length-1; i>0; i--){
        t2[i-1] = t2[i] * nums[i];
    }

    for(int i=0;i<nums.length;i++)
      {
        System.out.print(t1[i]+" "+t2[i]);
        System.out.println();
      }
 
    //multiply
    for(int i=0; i<nums.length; i++){
        result[i] = t1[i] * t2[i];
    }
 
    return result;
}

static int getsum(int[] bit,int ind)
{
  int sum=0;
  while(ind>0)
  {
    sum+=bit[ind];
    ind-= ind & (-ind);
  }

  return sum;
}

static void update(int[] bit,int max,int ind,int val)
{
  while(ind<=max)
  {
    bit[ind]+=val;
    ind+= ind & (-ind);
  }
}

    static ArrayList<Integer>[] adj;
    static int[] bfs(ArrayList<Integer>[] adj,int n,ArrayList<Integer> arr)
    {
      int[] vis=new int[n];
      int[] dis=new int[n];
      int[] par=new int[n];
      Queue<Integer> q=new LinkedList<>();

      Arrays.fill(dis,-1);

      for(int i=0;i<arr.size();i++)
      {
        vis[arr.get(i)]=1;
        dis[arr.get(i)]=0;
        par[arr.get(i)]=-1;
        q.add(arr.get(i));
      }

      while(!q.isEmpty())
      {
        int x=q.remove();
        for(int u:adj[x])
        {
          if(vis[u]==0)
          {
            vis[u]=1;
            dis[u]=dis[x]+1;
            par[u]=x;
            q.add(u);
          }
        }
      }

      return dis;
    }

    static boolean check(long mid,long a,long b)
    {
      long count=1;
      while(count<=mid)
      {
        count++;
        if(a<b)
          a+=count;
        else
          b+=count;

        if(a==b)
          return true;
      }
        return false;
    }

    static class a1
    {
      int p;
      int q;

      public a1(int p,int q)
      {
        this.p=p;
        this.q=q;
      }
    }
    static int get(int arr[], int n) 
    { 
        int result = 0; 
        int x, sum; 
          
        // Iterate through every bit 
        for(int i=0; i<32; i++) 
        { 
            // Find sum of set bits at ith position in all  
            // array elements 
            sum = 0; 
            x = (1 << i); 
            for(int j=0; j<n; j++) 
            { 
                if((arr[j] & x)!=0) 
                sum++; 
            } 
            // The bits with sum not multiple of 3, are the 
            // bits of element with single occurrence. 
            if ((sum % 3)!=0) 
            result |= x; 
        } 
        return result; 
    } 
    /*        Collections.sort(orders, new Comparator<Point>() {
            @Override
            public int compare(Point o1, Point o2) {
                if (o1.diff < o2.diff) {
                    return -1;
                } else if (o1.diff > o2.diff) {
                    return 1;
                } else {
                    return 0;
                }
            }
        });  */


    static boolean isPrime(int n)  
    {  
        // Corner cases  
        if (n <= 1) return false;  
        if (n <= 3) return true;  
          
        // This is checked so that we can skip  
        // middle five numbers in below loop  
        if (n % 2 == 0 || n % 3 == 0) return false;  
          
        for (int i = 5; i * i <= n; i = i + 6)  
            if (n % i == 0 || n % (i + 2) == 0)  
            return false;  
          
        return true;  
    }  
      
    static int nextPrime(int N)  
    {  
      
        // Base case  
        if (N <= 1)  
            return (2-N);  
      
        int prime = N;  
        boolean found = false;  
      
        // Loop continuously until isPrime returns  
        // true for a number greater than n  
        while (!found)  
        {  
            if (isPrime(prime))  
                {
                  found = true;
                  break;
                }  

            prime++;
        }  
      
        return (prime-N);  
    }  

    static final long INF = Long.MAX_VALUE/5;
    public static void main(String args[] ) throws Exception 
    {
        /* Enter your code here. Read input from STDIN. Print output to STDOUT */

        FastReader sc=new FastReader();
        int t=sc.nextInt();

        while(t-->0)
        {
          int b=sc.nextInt();
          int w=sc.nextInt();
          int flag=0;

          ArrayList<a1> res=new ArrayList<>();

          if(b<w)
          {
            flag=1;
            int temp=w;
            w=b;
            b=temp;
          }

          int x=2,y=2;

          while(w>0)
          {
            if((x+y)%2==0)
            {
              res.add(new a1(x,y));
              w--;
            }
            else
            {
              res.add(new a1(x,y));
              b--;
            }
            y++;
          }
          
          int cx=1, cy=2;
          while(b>0 && cy<=y)
          {
            res.add(new a1(cx,cy));
            b--;
            cy+=2;
          }

          cx = 3;
          cy = 2;
          while(b>0 && cy<=y)
          {
            res.add(new a1(cx,cy));
            b--;
            cy+=2;
           // System.out.println(b);
          }

         if (b > 0) 
         {
          res.add(new a1(2,1));
          b--; 
         }

        if (b > 0) 
        {
          b--;
          res.add(new a1(2,y));
       }

        if(b>0)
          System.out.println("NO");
        else
        {
          System.out.println("YES");

          for(int i=0;i<res.size();i++)
            System.out.println(res.get(i).p+ " "+ (res.get(i).q + flag));

        }




        }

 
        




      }

    }