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.InputStreamReader;
import java.util.*;

public class GameOutcome {
    static boolean test = false;

    public static void main(String[] args) throws IOException {

        initReader();
        logTime("");
        while (true) {

            logTime("Read:");
            solve();
            logTime("Solved:");

            if (!test)
                break;
        }

    }

    public static void solve() throws IOException {

        long test = nextLong();

        for (int i = 0; i < test; i++) {
            long n, k, d1, d2; // 10^12
            n = nextLong();
            k = nextLong();
            d1 = nextLong();
            d2 = nextLong();
            long max1 = Long.MAX_VALUE, max2 = Long.MAX_VALUE, max3 = Long.MAX_VALUE;

            long base = (k - d1 - d2);
            if (base >= 0 && base % 3 == 0)
                max1 = Math.max(base / 3 + d1, base / 3 + d2);
            base = (k - 2 * d1 + d2);
            if (d1 > d2 && base >= 0 && base % 3 == 0)
                max1 = Math.min(max1, base / 3 + d1);
            base = (k - 2 * d2 + d1);
            if (d2 >= d1 && base >= 0 && base % 3 == 0)
                max1 = Math.min(max1, base / 3 + d2);
            base = k - 2 * d1 - d2;
            if (base >= 0 && base % 3 == 0)
                max2 = base / 3 + d1 + d2;
            base = k - 2 * d2 - d1;
            if (base >= 0 && base % 3 == 0)
                max2 = Math.min(max2, base / 3 + d1 + d2);
            long min = Math.min(max1, max2);
            // max1 + " " + max2 + " - " +
            System.out.println((n % 3 == 0 && min <= n / 3 ? "yes" : "no"));
        }
    }

    /*****************************************************************
     ******************** BASIC READER *******************************
     *****************************************************************/

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    public static void initReader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
        return reader.readLine();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static Double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    /*****************************************************************
     ******************** TIME UTILITIES *******************************
     *****************************************************************/

    static long startTime = 0;
    static long preLogTime = 0;

    static void logTime(String lable) {
        if (!test)
            return;
        long current = System.currentTimeMillis();
        if (startTime != 0) {
            println(lable, " - From start:", (current - startTime),
                    "- From previous:", (current - preLogTime));
        } else {
            startTime = current;
        }
        preLogTime = current;
    }

    /*****************************************************************
     ******************** READ UTILITIES *******************************
     *****************************************************************/

    public static int[] readArray(int n) throws IOException {
        int[] result = new int[n];
        for (int i = 0; i < n; i++) {
            result[i] = nextInt();
        }
        return result;
    }

    public static long[] readArrayLong(int n) throws IOException {
        long[] result = new long[n];
        for (int i = 0; i < n; i++) {
            result[i] = nextLong();
        }
        return result;
    }

    public static int[][] readMatrix(int row, int column) throws IOException {
        int[][] result = new int[row][column];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < column; j++) {
                result[i][j] = nextInt();
            }
        }
        return result;
    }

    public static long[][] readMatrixLong(int row, int column)
            throws IOException {
        long[][] result = new long[row][column];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < column; j++) {
                result[i][j] = nextLong();
            }
        }
        return result;
    }

    /*****************************************************************
     ******************** PRINT UTILITIES *******************************
     *****************************************************************/

    public static void printTest(Object... obj) {
        if (!test)
            return;
        System.out.print(join(obj, " "));
    }

    public static void printTestLn(Object... obj) {
        if (!test)
            return;
        System.out.println(join(obj, " "));
    }

    public static void print(Object... obj) {
        System.out.print(join(obj, " "));
    }

    public static void println(Object... obj) {
        System.out.println(join(obj, " "));
    }

    public static String join(Object[] objs) {
        return join(objs, " ");
    }

    public static String join(int[] objs) {
        return join(objs, " ");
    }

    public static String join(long[] objs) {
        return join(objs, " ");
    }

    public static String join(Object[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static String join(int[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static String join(long[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static void printMatrix(int[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            println(join(matrix[i]));
        }
    }

    public static void printMatrix(long[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            println(join(matrix[i]));
        }
    }

    /*****************************************************************
     *************** ARRAY AND STRING UTILITIES **********************
     *****************************************************************/

    public static int[] initArray(int value, int length) {
        int[] result = new int[length];
        Arrays.fill(result, value);
        return result;
    }

    public static long[] initArray(long value, int length) {
        long[] result = new long[length];
        Arrays.fill(result, value);
        return result;
    }

    public static String initString(char c, int length) {
        char[] chars = new char[length];
        Arrays.fill(chars, c);
        return new String(chars);
    }
}
