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.InputStream;
import java.io.PrintWriter;
import java.util.HashSet;
import java.util.NoSuchElementException;
import java.util.Set;

public class Main {
	public static void main(String[] args) {
		new Main().solve();
		pw.close();
	}

	/**
	 * ASCII
	 * 0 48
	 * A 65
	 * a 97
	 */

	static PrintWriter pw = new PrintWriter(System.out);

	long MOD = 1_000_000_007;

	void solve() {
		FastScanner sc = new FastScanner();
		int t = sc.nextInt();
		for (int tc = 0; tc < t; tc++) {
			int a = sc.nextInt();
			int b = sc.nextInt();
			int c = sc.nextInt();
			int n = sc.nextInt();
			long sum = (long)a+b+c+n;
			long h = sum / 3;
			String ans = "NO";
			if (sum % 3 == 0 && a <= h && b <= h && c <= h) {
				ans = "YES";
			}
			out(ans);
		}
	}
	
	double getD(double x1, double x2, double y1, double y2) {
		return Math.sqrt(Math.pow(x1-x2,2) + Math.pow(y1-y2, 2));
	}

	int[][] d4 = new int[][] {{1,0},{0,1},{-1,0},{0,-1}};
	int[][] d8 = new int[][] {{1,0},{1,1},{0,1},{-1,1},{-1,0},{-1,-1},{0,-1},{1,-1}};

	class Data {
		int a;
		int b;
		int c;
		Data(int a, int b, int c) {
			this.a = a;
			this.b = b;
			this.c = c;
		}
		Data(int a, int b) {
			this.a = a;
			this.b = b;
		}
	}

	class Permutation {
		int[] array;

		Permutation(int N) {
			array = new int[N];
			for (int i = 0; i < N; i++) {
				array[i] = i+1;
			}
		}

		boolean nextPermutation() {
		    int i = array.length - 1;
		    while (i > 0 && array[i - 1] >= array[i])
		        i--;
		    if (i <= 0)
		        return false;

		    int j = array.length - 1;
		    while (array[j] <= array[i - 1])
		        j--;
		    int temp = array[i - 1];
		    array[i - 1] = array[j];
		    array[j] = temp;

		    j = array.length - 1;
		    while (i < j) {
		        temp = array[i];
		        array[i] = array[j];
		        array[j] = temp;
		        i++;
		        j--;
		    }
		    return true;
		}
	}

	class UnionFind {
		int[] parents;
		int[] counts;

		public UnionFind(int size) {
			parents = new int[size];
			counts = new int[size];
			for (int i = 0; i < size; i++) {
				parents[i] = i;
				counts[i] = 1;
			}
		}

		public int find(int a) {
			if (parents[a] == a) return a;
			parents[a] = find(parents[a]);
			return parents[a];
		}

		public void unite(int a, int b) {
			a = find(a);
			b = find(b);
			if (a == b) return;
			if (counts[a] < counts[b]) {
				parents[a] = b;
				counts[b] += counts[a];
			} else {
				parents[b] = a;
				counts[a] += counts[b];
			}
		}

		public boolean differ(int a, int b) {
			a = find(a);
			b = find(b);
			return a != b;
		}

		public int count(int a) {
			return counts[find(a)];
		}
	}

	class Combination {
		final int mod;
		final int max;

		final long[] fact;
		final long[] inv;
		final long[] invfact;

		public Combination(int n) {
			this(n, 1_000_000_007);
		}

		public Combination(int n, int mod) {
			this.mod = mod;
			max = n + 1;
			fact = new long[max];
			invfact = new long[max];
			inv = new long[max];

			inv[1] = 1;
			for (int i = 2; i < inv.length; i++) {
				inv[i] = inv[mod % i] * (mod - mod / i) % mod;
			}

			fact[0] = 1;
			invfact[0] = 1;
			for (int i = 1; i < inv.length; i++) {
				fact[i] = i * fact[i - 1] % mod;
				invfact[i] = inv[i] * invfact[i - 1] % mod;
			}
		}

		public long get(int n, int r) {
			return fact[n] * invfact[n - r] % mod * invfact[r] % mod;
		}

		public long gcd(long a, long b) {
			if (b == 0) return a;
			else {
				b %= MOD;
				if (b < 0) b+=MOD;
				return gcd(b, (b-a*inv[(int)b]%MOD*b%MOD)%MOD);
			}
		}
	}

	public long gcd(long a, long b) {
		if (b == 0) return a;
		else return gcd(b, a%b);
	}

	public void reverse(int[] a) {
		int last = a.length-1;
		int n = a.length / 2;
		for (int i = 0; i < n; i++) {
			int t = a[i];
			a[i] = a[last-i];
			a[last-i] = t;
		}
	}

	public void reverse(long[] a) {
		int last = a.length-1;
		int n = a.length / 2;
		for (int i = 0; i < n; i++) {
			long t = a[i];
			a[i] = a[last-i];
			a[last-i] = t;
		}
	}

	void out(String a) {
		pw.println(a);
	}
	void out(boolean a) {
		pw.println(a);
	}

	void out(int a) {
		pw.println(a);
	}

	void out(long a) {
		pw.println(a);
	}

	void out(double a) {
		pw.println(a);
	}

	void out(char a) {
		pw.println(a);
	}

	void rout(String a) {
		out(a);
		pw.close();
		System.exit(0);
	}
	void rout(int a) {
		out(a);
		pw.close();
		System.exit(0);
	}
	void rout(long a) {
		out(a);
		pw.close();
		System.exit(0);
	}
	void rout(double a) {
		out(a);
		pw.close();
		System.exit(0);
	}
	void rout(char a) {
		out(a);
		pw.close();
		System.exit(0);
	}
}


class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) {
            return true;
        } else {
            ptr = 0;
            try {
                buflen = in.read(buffer);
            } catch (IOException e) {
                e.printStackTrace();
            }
            if (buflen <= 0) {
                return false;
            }
        }
        return true;
    }

    private int readByte() {
        if (hasNextByte())
            return buffer[ptr++];
        else
            return -1;
    }

    private boolean isPrintableChar(int c) {
        return 33 <= c && c <= 126;
    }

    public boolean hasNext() {
        while (hasNextByte() && !isPrintableChar(buffer[ptr]))
            ptr++;
        return hasNextByte();
    }

    public String next() {
        if (!hasNext())
            throw new NoSuchElementException();
        StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (isPrintableChar(b)) {
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    public long nextLong() {
        if (!hasNext())
            throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {
            minus = true;
            b = readByte();
        }
        if (b < '0' || '9' < b) {
            throw new NumberFormatException();
        }
        while (true) {
            if ('0' <= b && b <= '9') {
                n *= 10;
                n += b - '0';
            } else if (b == -1 || !isPrintableChar(b)) {
                return minus ? -n : n;
            } else {
                throw new NumberFormatException();
            }
            b = readByte();
        }
    }

    public int nextInt() {
        long nl = nextLong();
        if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE)
            throw new NumberFormatException();
        return (int) nl;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }
}