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.math.BigInteger;
import java.util.*;
import java.util.Map.Entry;

import static java.lang.Math.*;

public class Main {
	public static void main(String[] args) throws Exception {
			solve();
	}
	

	public static void solve() throws IOException {
		FastScanner fscan = new FastScanner(System.in);
		BufferedWriter bw = new BufferedWriter(new OutputStreamWriter(System.out));
		
		int t = fscan.nextInt();
		nextCase:while(t-- > 0){
			final long n = fscan.nextLong(),
				k = fscan.nextLong(),
				d1 = fscan.nextLong(),
				d2 = fscan.nextLong();
			
			if(n%3 != 0) {
				bw.append("no\n");
				continue nextCase;
			}

			for (int s1 = -1; s1 <= 1; s1++) {
				for (int s2 = -1; s2 <= 1; s2++) {
					if(s1 == 0 || s2 == 0) {
						continue;
					}
					
					long td1 = s1 * d1;
					long td2 = s2 * d2;
					long x1 = (2*td1 + k + td2) / 3;
					long x2 = x1 - td1;
					long x3 = x2 - td2;
					
					if((2*td1 + k + td2)%3 != 0)
						continue;

						if(x1 >= 0 && x1 <= n/3 && x2>=0 && x2 <= n/3 && x3>= 0 && x3 <= n/3){
							if ((s1 > 0 && x1 >= x2 && s2 > 0 && x2 >= x3)||
							(s1 > 0 && x1 >= x2 && s2 < 0 && x2 <= x3)||
							(s1 < 0 && x1 <= x2 && s2 > 0 && x2 >= x3)||
							(s1 < 0 && x1 <= x2 && s2 < 0 && x2 <= x3)
							){
								bw.append("yes\n");
								continue nextCase;
							}
						}
				}
			}
			bw.append("no\n");
		}
				
		bw.close();
	}
	
	
}






class IO {
	public static void readIntArray(int a[], int N, FastScanner fscan)
			throws IOException {
		readIntArray(a, N, 0, fscan);
	}

	public static void readIntArray(int a[], int N, int start, FastScanner fscan)
			throws IOException {
		for (int i = 0; i < N; i++) {
			a[start + i] = fscan.nextInt();
		}
	}

	public static void readArray(long a[], int N, FastScanner fscan)
			throws IOException {
		readArray(a, N, 0, fscan);
	}

	public static void readArray(long a[], int N, int start, FastScanner fscan)
			throws IOException {
		for (int i = 0; i < N; i++) {
			a[start + i] = fscan.nextInt();
		}
	}
}

class FastScanner {
	InputStream is;
	byte buff[] = new byte[1024];
	int currentChar = -1;
	int buffChars = 0;

	public FastScanner(InputStream inputStream) {
		is = inputStream;
	}

	public boolean hasNext() throws IOException {
		return currentChar == -1 || buffChars > 0;
	}

	public char nextChar() throws IOException {
		// if we already have that next char read, just return else input
		if (currentChar == -1 || currentChar >= buffChars) {
			currentChar = 0;
			buffChars = is.read(buff);
		}

		if (buffChars <= 0) {
			throw new RuntimeException("No char found...");
		}

		int ch;
		while (isSpace(ch = nextCharAsInt()))
			;
		return (char) ch;
	}

	public int nextCharAsInt() throws IOException {
		// if we already have that next char read, just return else input
		if (currentChar == -1 || currentChar >= buffChars) {
			currentChar = 0;
			buffChars = is.read(buff);
		}

		if (buffChars <= 0) {
			return -1;
		}
		return (char) buff[currentChar++];
	}

	public String nextLine() throws IOException {
		StringBuilder bldr = new StringBuilder();
		int ch;
		while (isLineEnd(ch = nextCharAsInt()))
			// ignore empty lines ???
			;

		do {
			bldr.append((char) ch);
		} while (!isLineEnd(ch = nextCharAsInt()));

		return bldr.toString();
	}

	public String nextString() throws IOException {
		StringBuilder bldr = new StringBuilder();
		int ch;
		while (isSpace(ch = nextCharAsInt()))
			;

		do {
			bldr.append((char) ch);
		} while (!isSpace(ch = nextCharAsInt()));

		return bldr.toString();
	}

	public int nextInt() throws IOException {
		// considering ASCII files--> 8 bit chars, unicode files has 16 bit
		// chars (byte1 then byte2)
		int result = 0;
		int sign = 1;
		int ch;
		while (isSpace(ch = nextCharAsInt()))
			;

		if (ch == '-') {
			sign = -1;
			ch = nextCharAsInt();
		}

		do {
			if (ch < '0' || ch > '9')
				throw new NumberFormatException("Found '" + ch
						+ "' while parsing for int.");

			result *= 10;
			result += ch - '0';
		} while (!isSpace(ch = nextCharAsInt()));

		return sign * result;
	}

	public long nextLong() throws IOException {
		// considering ASCII files--> 8 bit chars, unicode files has 16 bit
		// chars (byte1 then byte2)
		long result = 0;
		int sign = 1;
		int ch;
		while (isSpace(ch = nextCharAsInt()))
			;

		if (ch == '-') {
			sign = -1;
			ch = nextCharAsInt();
		}

		do {
			if (ch < '0' || ch > '9')
				throw new NumberFormatException("Found '" + ch
						+ "' while parsing for int.");

			result *= 10;
			result += ch - '0';
		} while (!isSpace(ch = nextCharAsInt()));

		return sign * result;
	}

	private boolean isLineEnd(int ch) {
		return ch == '\n' || ch == '\r' || ch == -1;
	}

	private boolean isSpace(int ch) {
		return ch == '\n' || ch == ' ' || ch == '\t' || ch == '\r' || ch == -1;
	}

	public void close() throws IOException {
		is.close();
	}
}
