Problem: Polycarp has three sisters: Alice, Barbara, and Cerene. They're collecting coins. Currently, Alice has a coins, Barbara has b coins and Cerene has c coins. Recently Polycarp has returned from the trip around the world and brought n coins.

He wants to distribute all these n coins between his sisters in such a way that the number of coins Alice has is equal to the number of coins Barbara has and is equal to the number of coins Cerene has. In other words, if Polycarp gives A coins to Alice, B coins to Barbara and C coins to Cerene (A+B+C=n), then a + A = b + B = c + C.

Note that A, B or C (the number of coins Polycarp gives to Alice, Barbara and Cerene correspondingly) can be 0.

Your task is to find out if it is possible to distribute all n coins between sisters in a way described above.

You have to answer t independent test cases.

Input

The first line of the input contains one integer t (1 ≤ t ≤ 10^4) — the number of test cases.

The next t lines describe test cases. Each test case is given on a new line and consists of four space-separated integers a, b, c and n (1 ≤ a, b, c, n ≤ 10^8) — the number of coins Alice has, the number of coins Barbara has, the number of coins Cerene has and the number of coins Polycarp has.

Output

For each test case, print "YES" if Polycarp can distribute all n coins between his sisters and "NO" otherwise.

Example

Input


5
5 3 2 8
100 101 102 105
3 2 1 100000000
10 20 15 14
101 101 101 3


Output


YES
YES
NO
NO
YES

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.util.*;
import java.math.*;
import java.io.*;
import java.text.*;
import java.math.BigInteger;
 
public class Main
{  
 
    //Life's a bitch
    public static boolean[] sieve(long n)
    {
        boolean[] prime = new boolean[(int)n+1];
        Arrays.fill(prime,true);
        prime[0] = false;
        prime[1] = false;
        long m = (long)Math.sqrt(n);
        for(int i=2;i<=m;i++)
        {
            if(prime[i])
            {
                for(int k=i*i;k<=n;k+=i)
                {
                    prime[k] = false;
                }
            }
        }
        return prime;
    } 
 
    
    static long GCD(long a,long b)
    {
        if(b==0)
        {
            return a;
        }
        return GCD(b,a%b);
    }
 
    static long CountCoPrimes(long n)
    {
        long res = n;
        for(int i=2;i*i<=n;i++)
        {
            if(n%i==0)
            {
                while(n%i==0)
                {
                    n/=i;
                }
                res-=res/i;
            }
        }
        if(n>1)
        {
            res-=res/n;
        }
        return res;
    }
 
 
    
 
    
 
    static boolean prime(int n)
    {
        for(int i=2;i*i<=n;i++)
        {
            if(n%i==0)
            {
                return false;
            }
        }
        return true;
    }

    
 
   
 
 
   
   
  
    public static void main(String[] args) throws IOException
    {
     
        new Main().run();
       
    }
 
 	static void reverse(int[] a,int start,int end)
 	{	
 		
 		while(start<end)
 		{
 			int temp = a[start];
 			a[start] = a[end];
 			a[end] = temp;
 			start++;
 			end--;
 		}
 	}

 	static long LCM(long a,long b)
 	{
 		return (a*b)/GCD(a,b);
 	}
   
 
    Scanner in = new Scanner(System.in);
    // static int[] arr,tree[],lev;
    void run() throws IOException
    {
    	
      int t = ni();
      while(t-->0)
      {
      	 long a = nl();
      	 long b = nl();
      	 long c = nl();
      	 long d = nl();
      	 long max = max(a,max(b,c));
      	 d-=max-a;
      	 d-=max-b;
      	 d-=max-c;
      	 if(d<0 || d%3!=0)
      	 {
      	 	printS("NO");
      	  	continue;
      	 }

      	 printS("YES");



      	 
      	

      		
      	
      }



    	
   	}

    



   
    
    


   	




  

   	

 	

   	
	


	
	


   

 

    
 
 
 
 
 
 
    
 
    //xor range query
    static long xor(long n)
    {
 
        if(n%4==0)
        {
            return n;
        }
        if(n%4==1)
        {
            return  1;
        }
        if(n%4==2)
        {
            return n+1;
        }
        return 0;
    }
 
    static long xor(long a,long b)
    {
        return xor(b)^xor(a-1);
    }
 
 
    
 
  
   
    
 
    
       
    
 
    
   
  
 
 
 
   
 
     void printL(long a)
    {
        System.out.println(a);
    }
    void printS(String s)
    {
        System.out.println(s);
    }
 
     void printD(Double d)
    {
        System.out.println(d);
    }
  
   
   
    static void swap(char[] c,int a,int b)
    {
        char t = c[a];
        c[a] = c[b];
        c[b] = t;
    }
 
    static long max(long n,long m)
    {
        return Math.max(n,m);
    }
    static long min(long n,long m)
    {
        return Math.min(n,m);
    }
 
    double nd() throws IOException
    {
        return Double.parseDouble(in.next());
    }
    int ni() throws IOException
    {
        return Integer.parseInt(in.next());
    }
 
    long nl() throws IOException
    {
        return Long.parseLong(in.next());
    }
 
    String si() throws IOException
    {
        return in.next();
    }
 
 
  
   
    static long abs(long n)
    {
        return Math.abs(n);
    }
 
    static class Scanner 
    {
        StringTokenizer st;
        BufferedReader br;
 
        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 boolean ready() throws IOException {return br.ready();}
 
 
    }
 
    
}
 
 
 
class Pair implements Comparable<Pair>
{
   int x,y;
    public Pair(int x,int y)
    {
        this.x = x;
        this.y = y;
    }
    public int compareTo(Pair o)
    {
        return this.y-o.y;
    }
}