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.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.lang.reflect.Constructor;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collection;
import java.util.InputMismatchException;
import java.util.StringTokenizer;

public class CodeG {
  static long n, k, d1, d2;

  static boolean caseOne() {
    long a = d1 + d2;
    long b = d2;
    long c = 0;
    long remaining = k - a - b - c;
    if (remaining < 0) {
      return false;
    }
    if(remaining % 3 != 0) {
      return false;
    }
    a += remaining / 3;
    b += remaining / 3;
    c += remaining / 3;
    remaining = n - k;
    long max = Math.max(a, b);
    max = Math.max(max, c);
    remaining -= max - a;
    remaining -= max - b;
    remaining -= max - c;
    if (Math.abs(a - b) != d1) {
      return false;
    }
    if (Math.abs(b - c) != d2) {
      return false;
    }
    a = max + remaining / 3;
    b = max + remaining / 3;
    c = max + remaining / 3;
    return remaining >= 0 && ((remaining % 3) == 0) && (a + b + c) == n;
  }

  static boolean caseTwo() {
    long a = 0;
    long b = d1;
    long c = d1 - d2;
    if (c < 0) {
      a -= c;
      b -= c;
      c = 0;
    }
    long remaining = k - a - b - c;
    if (remaining < 0) {
      return false;
    }
    if(remaining % 3 != 0) {
      return false;
    }
    a += remaining / 3;
    b += remaining / 3;
    c += remaining / 3;
    remaining = n - k;
    long max = Math.max(a, b);
    max = Math.max(max, c);
    remaining -= max - a;
    remaining -= max - b;
    remaining -= max - c;
    if (Math.abs(a - b) != d1) {
      return false;
    }
    if (Math.abs(b - c) != d2) {
      return false;
    }
    a = max + remaining / 3;
    b = max + remaining / 3;
    c = max + remaining / 3;
    return remaining >= 0 && ((remaining % 3) == 0) && (a + b + c) == n;
}

  static boolean caseThree() {
    long a = 0;
    long b = d1;
    long c = d1 + d2;
    long remaining = k - a - b - c;
    if (remaining < 0) {
      return false;
    }
    if(remaining % 3 != 0) {
      return false;
    }
    a += remaining / 3;
    b += remaining / 3;
    c += remaining / 3;
    remaining = n - k;
    long max = Math.max(a, b);
    max = Math.max(max, c);
    remaining -= max - a;
    remaining -= max - b;
    remaining -= max - c;
    if (Math.abs(a - b) != d1) {
      return false;
    }
    if (Math.abs(b - c) != d2) {
      return false;
    }
    a = max + remaining / 3;
    b = max + remaining / 3;
    c = max + remaining / 3;
    return remaining >= 0 && ((remaining % 3) == 0) && (a + b + c) == n;
}

  static boolean caseFour() {
    long a = d1;
    long b = 0;
    long c = d2;
    long remaining = k - a - b - c;
    if (remaining < 0) {
      return false;
    }
    if(remaining % 3 != 0) {
      return false;
    }
    a += remaining / 3;
    b += remaining / 3;
    c += remaining / 3;
    remaining = n - k;
    long max = Math.max(a, b);
    max = Math.max(max, c);
    remaining -= max - a;
    remaining -= max - b;
    remaining -= max - c;
    if (Math.abs(a - b) != d1) {
      return false;
    }
    if (Math.abs(b - c) != d2) {
      return false;
    }
    a = max + remaining / 3;
    b = max + remaining / 3;
    c = max + remaining / 3;
    return remaining >= 0 && ((remaining % 3) == 0) && (a + b + c) == n;
}
  
  public static void main(String[] args) {
    Scanner sc = new SuperScanner();
    int x = sc.nextInt();
    for (int i = 0; i < x; i++) {
      n = sc.nextLong();
      k = sc.nextLong();
      d1 = sc.nextLong();
      d2 = sc.nextLong();
      System.out.println(caseOne() || caseTwo() || caseThree() || caseFour()  ? "yes" : "no");
    }
  }

  static class SuperScanner extends Scanner {
    private InputStream stream;
    private byte[] buf = new byte[8096];
    private int curChar;
    private int numChars;

    public SuperScanner() {
        this.stream = System.in;
    }

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }
    
    public static boolean isWhitespace(int c) {
      return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
    }
    
    private final StringBuilder sb = new StringBuilder();
    
    @Override
    public String next() {
      int c = read();
      while (isWhitespace(c)) {
          if (c == -1) {
            return null;
          }
          c = read();
      }
      sb.setLength(0);
      do {
          sb.append((char) c);
          c = read();
      } while (!isWhitespace(c));
      return sb.toString();
    }

    @Override
    public int nextInt() {
        int c = read();
        while (isWhitespace(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res = (res << 3) + (res << 1);
            res += c - '0';
            c = read();
        } while (!isWhitespace(c));
        return res * sgn;
    }

    @Override
    public long nextLong() {
        int c = read();
        while (isWhitespace(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        long res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res = (res << 3) + (res << 1);
            res += c - '0';
            c = read();
        } while (!isWhitespace(c));
        return res * sgn;
    }
  }
  
  static class Scanner {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    StringTokenizer st = new StringTokenizer("");

    public String nextLine() {
      try {
        return br.readLine();
      } catch (Exception e) {
        throw (new RuntimeException());
      }
    }

    public int nextIntOrQuit() {
      Integer n = nextInteger();
      if (n == null) {
        System.exit(0);
      }
      return n.intValue();
    }

    public String next() {
      while (!st.hasMoreTokens()) {
        String l = nextLine();
        if (l == null)
          return null;
        st = new StringTokenizer(l);
      }
      return st.nextToken();
    }

    public int nextInt() {
      return Integer.parseInt(next());
    }

    public long nextLong() {
      return Long.parseLong(next());
    }

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

    public int[] nextIntArray(int n) {
      int[] res = new int[n];
      for (int i = 0; i < res.length; i++)
        res[i] = nextInt();
      return res;
    }

    public long[] nextLongArray(int n) {
      long[] res = new long[n];
      for (int i = 0; i < res.length; i++)
        res[i] = nextLong();
      return res;
    }

    public double[] nextDoubleArray(int n) {
      double[] res = new double[n];
      for (int i = 0; i < res.length; i++)
        res[i] = nextDouble();
      return res;
    }

    public void sortIntArray(int[] array) {
      Integer[] vals = new Integer[array.length];
      for (int i = 0; i < array.length; i++)
        vals[i] = array[i];
      Arrays.sort(vals);
      for (int i = 0; i < array.length; i++)
        array[i] = vals[i];
    }

    public void sortLongArray(long[] array) {
      Long[] vals = new Long[array.length];
      for (int i = 0; i < array.length; i++)
        vals[i] = array[i];
      Arrays.sort(vals);
      for (int i = 0; i < array.length; i++)
        array[i] = vals[i];
    }

    public void sortDoubleArray(double[] array) {
      Double[] vals = new Double[array.length];
      for (int i = 0; i < array.length; i++)
        vals[i] = array[i];
      Arrays.sort(vals);
      for (int i = 0; i < array.length; i++)
        array[i] = vals[i];
    }

    public String[] nextStringArray(int n) {
      String[] vals = new String[n];
      for (int i = 0; i < n; i++)
        vals[i] = next();
      return vals;
    }

    public Integer nextInteger() {
      String s = next();
      if (s == null)
        return null;
      return Integer.parseInt(s);
    }

    public int[][] nextIntMatrix(int n, int m) {
      int[][] ans = new int[n][];
      for (int i = 0; i < n; i++)
        ans[i] = nextIntArray(m);
      return ans;
    }

    public char[][] nextGrid(int r) {
      char[][] grid = new char[r][];
      for (int i = 0; i < r; i++)
        grid[i] = next().toCharArray();
      return grid;
    }

    public static <T> T fill(T arreglo, int val) {
      if (arreglo instanceof Object[]) {
        Object[] a = (Object[]) arreglo;
        for (Object x : a)
          fill(x, val);
      } else if (arreglo instanceof int[])
        Arrays.fill((int[]) arreglo, val);
      else if (arreglo instanceof double[])
        Arrays.fill((double[]) arreglo, val);
      else if (arreglo instanceof long[])
        Arrays.fill((long[]) arreglo, val);
      return arreglo;
    }

    public <T> T[] nextObjectArray(Class<T> clazz, int size) {
      @SuppressWarnings("unchecked")
      T[] result = (T[]) java.lang.reflect.Array.newInstance(clazz, size);
      for (int c = 0; c < 3; c++) {
        Constructor<T> constructor;
        try {
          if (c == 0)
            constructor = clazz.getDeclaredConstructor(Scanner.class,
                Integer.TYPE);
          else if (c == 1)
            constructor = clazz.getDeclaredConstructor(Scanner.class);
          else
            constructor = clazz.getDeclaredConstructor();
        } catch (Exception e) {
          continue;
        }
        try {
          for (int i = 0; i < result.length; i++) {
            if (c == 0)
              result[i] = constructor.newInstance(this, i);
            else if (c == 1)
              result[i] = constructor.newInstance(this);
            else
              result[i] = constructor.newInstance();
          }
        } catch (Exception e) {
          throw new RuntimeException(e);
        }
        return result;
      }
      throw new RuntimeException("Constructor not found");
    }

    public void printLine(int... vals) {
      if (vals.length == 0)
        System.out.println();
      else {
        System.out.print(vals[0]);
        for (int i = 1; i < vals.length; i++)
          System.out.print(" ".concat(String.valueOf(vals[i])));
        System.out.println();
      }
    }

    public void printLine(long... vals) {
      if (vals.length == 0)
        System.out.println();
      else {
        System.out.print(vals[0]);
        for (int i = 1; i < vals.length; i++)
          System.out.print(" ".concat(String.valueOf(vals[i])));
        System.out.println();
      }
    }

    public void printLine(double... vals) {
      if (vals.length == 0)
        System.out.println();
      else {
        System.out.print(vals[0]);
        for (int i = 1; i < vals.length; i++)
          System.out.print(" ".concat(String.valueOf(vals[i])));
        System.out.println();
      }
    }

    public void printLine(int prec, double... vals) {
      if (vals.length == 0)
        System.out.println();
      else {
        System.out.printf("%." + prec + "f", vals[0]);
        for (int i = 1; i < vals.length; i++)
          System.out.printf(" %." + prec + "f", vals[i]);
        System.out.println();
      }
    }

    public Collection<Integer> wrap(int[] as) {
      ArrayList<Integer> ans = new ArrayList<Integer>();
      for (int i : as)
        ans.add(i);
      return ans;
    }

    public int[] unwrap(Collection<Integer> collection) {
      int[] vals = new int[collection.size()];
      int index = 0;
      for (int i : collection)
        vals[index++] = i;
      return vals;
    }
  }
}