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.util.* ;
import java.lang.* ;
import java.io.*;

public class javaTemplate {
	
	static FastReader sc = new FastReader();
	//	static Scanner sc = new Scanner(System.in) ;
	
	public static void main(String[] args) {
		
		
  
        int t = sc.nextInt() ;
		
		while(t -- != 0) {
			long a = sc.nextLong() ;
			long b = sc.nextLong() ;
			long c = sc.nextLong() ;
			long n = sc.nextLong() ;
			
			long max = Math.max(Math.max(a, b), Math.max(b, c)) ;
			long diff = 0 ;
			if(max != a) {
				diff += Math.abs(max-a) ;
			}
			if(max != b) {
				diff += Math.abs(max-b) ;
			}
			if(max != c) {
				diff += Math.abs(max-c) ;
			}
			
			if(n-diff >= 0) {
				n = n-diff ;
				long ftotal = (long)Math.ceil(n/(double)3) ;
				if(ftotal*3 == n) {
					System.out.println("YES");
				} else {
					System.out.println("NO");
				}
			} else {
				System.out.println("NO");
			}
			
			
		}
		
		
		
		
	}
	

	
	

	

	
	
	

	
	
	
	
	
	
	 
	
	


	
	
//_________________________//Template//_____________________________________________________________________
	
	
		//		FAST I/O
		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;
	        }
		}
	
	
		
		
		
		
		
		
		
		// Modulo
		static int mod(int a, int m)
		{
		    return (a%m + m) % m;
		}
		
		
		
		
		
		//		LPS Array
		static void LPSArray(String pat, int M, int lps[]) {
			int i = 1 ;
			int length = 0 ;
			lps[0] = 0 ;
			
			while(i < M) {
				if(pat.charAt(i) == pat.charAt(length)) {
					length ++ ;
					lps[i] = length ;
					i ++ ;
				} else if(length != 0) {
					length = lps[length-1] ;
				} else {
					lps[i] = length ;
					i ++ ;
				}
			}
		}
		
		
		
		//		KMP Search
		static boolean kmpSearch(String pat, String txt) {
			boolean val = false ;
			int M = pat.length() ;
			int N = txt.length() ;
			
			int lps[] = new int[M] ;
			
			int j = 0 ;
			int i = 0 ;
			
			LPSArray(pat,M,lps) ;
			
			while(i < N) {
				if(pat.charAt(j) == txt.charAt(i)) {
					i ++ ;
					j ++ ;
				} else if(j != 0) {
					j = lps[j-1] ;
				} else {
					i ++ ;
				}
				
				if(j == M) {
					 val = true ;
					 j = lps[j-1] ;
				}
			}
			
			return val ;
		}
	
	
		
			
			
		
		
		
		//		Palindrom or Not
		static boolean isPalindrome(StringBuilder str, int low, int high) {
					
					while (low < high) {
						if (str.charAt(low) != str.charAt(high)) return false;
					 	low++;
					 	high--;
					}
					return true;
				}
	
	
		// Euler Tortient fx
	static int Phi(int n) {
		
		int count = 0 ;
		for(int i = 1 ; i< n ; i++) {
			if(GCD(i,n) == 1) count ++ ;
		}
		return count ;
	}
	
	
	
		// Integer Sort
		static void sort(int[] a) 
		   {
				ArrayList<Integer> l=new ArrayList<>();
				for (int i:a) l.add(i);
				Collections.sort(l);
				for (int i=0; i<a.length; i++) a[i]=l.get(i);
			}
	
		
		
		
		// Long Sort
		static void sort(long[] a) 
		   {
				ArrayList<Long> l=new ArrayList<>();
				for (long i:a) l.add(i);
				Collections.sort(l);
				for (int i=0; i<a.length; i++) a[i]=l.get(i);
			}
	
	
		
		// boolean Value
		static void val(boolean val)
	    {
	       System.out.println(val ? "YES" : "NO");
	       System.out.flush();
	    }
	
	
		
	
		// GCD
		public static int GCD(int a , int b) {
				if(b == 0) return a ;
				
				return GCD(b, a%b) ;
			}
	
		
		
		
		
		
		// sieve
		public static boolean [] sieveofEratosthenes(int n) {
			
			boolean isPrime[] = new boolean[n+1] ;
			Arrays.fill(isPrime, true);
			isPrime[0] = false ;
			isPrime[1] = false ;
			
			for(int i = 2 ; i * i <= n ; i++) {
				
				for(int j = 2 * i ; j<= n ; j+= i) {
					isPrime[j] = false ;
				}
			}
			
			return isPrime ;
		}
		
		
		
		
		// fastPower
		public static long fastPowerModulo(long a, long b, long n) {
			
			long res = 1 ;
			
			while(b > 0) {
			if((b&1) != 0) {
				res = (res * a % n) % n ;
			}
			
			a = (a % n * a % n) % n ;
			b = b >> 1 ;
			}
			
			return res ;
		}
	

}