There are n games in a football tournament. Three teams are participating in it. Currently k games had already been played. 

You are an avid football fan, but recently you missed the whole k games. Fortunately, you remember a guess of your friend for these k games. Your friend did not tell exact number of wins of each team, instead he thought that absolute difference between number of wins of first and second team will be d1 and that of between second and third team will be d2.

You don't want any of team win the tournament, that is each team should have the same number of wins after n games. That's why you want to know: does there exist a valid tournament satisfying the friend's guess such that no team will win this tournament?

Note that outcome of a match can not be a draw, it has to be either win or loss.

Input

The first line of the input contains a single integer corresponding to number of test cases t (1 ≤ t ≤ 105).

Each of the next t lines will contain four space-separated integers n, k, d1, d2 (1 ≤ n ≤ 1012; 0 ≤ k ≤ n; 0 ≤ d1, d2 ≤ k) — data for the current test case.

Output

For each test case, output a single line containing either "yes" if it is possible to have no winner of tournament, or "no" otherwise (without quotes).

Examples

Input

5
3 0 0 0
3 3 0 0
6 4 1 0
6 3 3 0
3 3 3 2


Output

yes
yes
yes
no
no

Note

Sample 1. There has not been any match up to now (k = 0, d1 = 0, d2 = 0). If there will be three matches (1-2, 2-3, 3-1) and each team wins once, then at the end each team will have 1 win.

Sample 2. You missed all the games (k = 3). As d1 = 0 and d2 = 0, and there is a way to play three games with no winner of tournament (described in the previous sample), the answer is "yes".

Sample 3. You missed 4 matches, and d1 = 1, d2 = 0. These four matches can be: 1-2 (win 2), 1-3 (win 3), 1-2 (win 1), 1-3 (win 1). Currently the first team has 2 wins, the second team has 1 win, the third team has 1 win. Two remaining matches can be: 1-2 (win 2), 1-3 (win 3). In the end all the teams have equal number of wins (2 wins).
import java.io.*;
import java.util.*;

/**
 * @author master_j
 * @version 0.4
 * @since May 3, 2014
 */
public class Main {
    long n, k, n3;

    private void solve() throws IOException {
        int t = io.nI();
        for(int i = 0; i < t; i++){
            n = io.nL();
            k = io.nL();
            n3 = n / 3;
            io.wln(solve(io.nL(), io.nL()) ? "yes" : "no");
        }

    }//2.2250738585072012e-308

    private boolean solve(long d10, long d20){
        if(n % 3 != 0)
            return false;

        if(d10 != 0 && d20 != 0) {
            for (long d1 = -d10; d1 <= d10; d1 += 2 * d10)
                for (long d2 = -d20; d2 <= d20; d2 += 2 * d20)
                    if (solve0(d1, d2))
                        return true;
            return false;
        }

        if(d10 == 0 && d20 != 0) {
            for (long d2 = -d20; d2 <= d20; d2 += 2 * d20)
                if (solve0(0, d2))
                    return true;
            return false;
        }

        if(d10 != 0 && d20 == 0) {
            for (long d1 = -d10; d1 <= d10; d1 += 2 * d10)
                if (solve0(d1, 0))
                    return true;
            return false;
        }

        return solve0(0, 0);
    }

    private boolean solve0(long d1, long d2){
        long x1 = (k - (2*d1 + d2));
        if(x1 % 3 != 0)
            return false;
        x1 /= 3;
        long x2 = x1 + d1;
        long x3 = x2 + d2;
        if(x1 < 0 || x2 < 0 || x3 < 0)
            return false;
        if(x1 + x2 + x3 != k)
            return false;
        long k1 = n / 3 - x1;
        long k2 = n / 3 - x2;
        long k3 = n / 3 - x3;
        if(k1 < 0 || k2 < 0 || k3 < 0)
            return false;
        if(k1 + k2 + k3 != n - k)
            return false;
        return true;
    }

    public static void main(String[] args) throws IOException {
        IO.launchSolution(args);
    }

    Main(IO io) throws IOException {
        this.io = io;
        solve();
    }

    private final IO io;
}

class IO {
    static final String _localArg = "master_j";
    private static final String _problemName = "";
    private static final IO.Mode _inMode = Mode.STD_;
    private static final IO.Mode _outMode = Mode.STD_;
    private static final boolean _autoFlush = false;

    static enum Mode {STD_, _PUT_TXT, PROBNAME_}

    private final StreamTokenizer st;
    private final BufferedReader br;
    private final Reader reader;

    private final PrintWriter pw;
    private final Writer writer;

    static void launchSolution(String[] args) throws IOException {
        boolean local = (args.length == 1 && args[0].equals(IO._localArg));
        IO io = new IO(local);

        long nanoTime = 0;
        if (local) {
            nanoTime -= System.nanoTime();
            io.wln("<output>");
        }

        io.flush();
        new Main(io);
        io.flush();

        if(local){
            io.wln("</output>");
            nanoTime += System.nanoTime();
            final long D9 = 1000000000, D6 = 1000000, D3 = 1000;
            if(nanoTime >= D9)
                io.wf("%d.%d seconds\n", nanoTime/D9, nanoTime%D9);
            else if(nanoTime >= D6)
                io.wf("%d.%d millis\n", nanoTime/D6, nanoTime%D6);
            else if(nanoTime >= D3)
                io.wf("%d.%d micros\n", nanoTime/D3, nanoTime%D3);
            else
                io.wf("%d nanos\n", nanoTime);
        }

        io.close();
    }

    IO(boolean local) throws IOException {
        if(_inMode == Mode.PROBNAME_ || _outMode == Mode.PROBNAME_)
            if(_problemName.length() == 0)
                throw new IllegalStateException("You imbecile. Where's my <_problemName>?");

        if(_problemName.length() > 0)
            if(_inMode != Mode.PROBNAME_ && _outMode != Mode.PROBNAME_)
                throw new IllegalStateException("You imbecile. What's the <_problemName> for?");

        Locale.setDefault(Locale.US);

        if (local) {
            reader = new FileReader("input.txt");
            writer = new OutputStreamWriter(System.out);
        } else {
            switch (_inMode) {
                case STD_:
                    reader = new InputStreamReader(System.in);
                    break;
                case PROBNAME_:
                    reader = new FileReader(_problemName + ".in");
                    break;
                case _PUT_TXT:
                    reader = new FileReader("input.txt");
                    break;
                default:
                    throw new NullPointerException("You imbecile. Gimme _inMode.");
            }
            switch (_outMode) {
                case STD_:
                    writer = new OutputStreamWriter(System.out);
                    break;
                case PROBNAME_:
                    writer = new FileWriter(_problemName + ".out");
                    break;
                case _PUT_TXT:
                    writer = new FileWriter("output.txt");
                    break;
                default:
                    throw new NullPointerException("You imbecile. Gimme _outMode.");
            }
        }

        br = new BufferedReader(reader);
        st = new StreamTokenizer(br);

        pw = new PrintWriter(writer, _autoFlush);

        if(local && _autoFlush)
            wln("Note: auto-flush is on.");
    }

    void wln()          {pw.println(); }
    void wln(boolean x) {pw.println(x);}
    void wln(char x)    {pw.println(x);}
    void wln(char x[])  {pw.println(x);}
    void wln(double x)  {pw.println(x);}
    void wln(float x)   {pw.println(x);}
    void wln(int x)     {pw.println(x);}
    void wln(long x)    {pw.println(x);}
    void wln(Object x)  {pw.println(x);}
    void wln(String x)  {pw.println(x);}

    void wf(String f, Object...o){pw.printf(f, o);}

    void w(boolean x)   {pw.print(x);}
    void w(char x)      {pw.print(x);}
    void w(char x[])    {pw.print(x);}
    void w(double x)    {pw.print(x);}
    void w(float x)     {pw.print(x);}
    void w(int x)       {pw.print(x);}
    void w(long x)      {pw.print(x);}
    void w(Object x)    {pw.print(x);}
    void w(String x)    {pw.print(x);}

    int nI() throws IOException    {st.nextToken(); return (int)st.nval;}
    double nD() throws IOException {st.nextToken(); return st.nval;}
    float nF() throws IOException  {st.nextToken(); return (float)st.nval;}
    long nL() throws IOException   {st.nextToken(); return (long)st.nval;}
    String nS() throws IOException {st.nextToken(); return st.sval;}

    void wc(String x){ wc(x.toCharArray()); }
    void wc(char c1, char c2){for(char c = c1; c<=c2; c++)wc(c);}
    void wc(char x[]){
        for(char c : x)
            wc(c);
    }
    void wc(char x){st.ordinaryChar(x); st.wordChars(x, x);}

    public boolean eof() {return st.ttype == StreamTokenizer.TT_EOF;}
    public boolean eol() {return st.ttype == StreamTokenizer.TT_EOL;}

    void flush(){pw.flush();}
    void close() throws IOException{reader.close(); br.close(); flush(); pw.close();}
}