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.*;
import java.util.*;
public class Main
{
    static long mod=((long)1e9)+7;//toString
    public static int gcd(int a,int b){if(b==0)return a;else return gcd(b,a%b);}
    public static long pow_mod(long x,long y){long res=1;x=x%mod;while(y > 0){if((y & 1)==1)res=(res * x)%mod;y=y>>1;x =(x * x)%mod;}return res;}
    public static int lower_bound(int[]arr,int val){int lo=0;int hi=arr.length-1;while(lo<hi){int mid=lo+((hi-lo+1)/2);if(arr[mid]==val){return mid;}else if(arr[mid]>val){hi=mid-1;}else lo=mid;}if(arr[lo]<=val)return lo;else return -1;}
    public static int upper_bound(int[]arr,int val){int lo=0;int hi=arr.length-1;while(lo<hi){int mid=lo+((hi-lo)/2);if(arr[mid]==val){return mid;}else if(arr[mid]>val){hi=mid;;}else lo=mid+1;}if(arr[lo]>=val)return lo;else return -1;}
    public static long first( long d1, long d2, long a, long b ){
        long ans = 0;long x = -1;
        if( ( a - ( ( 2 * d1 ) + d2 ) ) > -1 ){
            if( ( a - ( ( 2 * d1 ) + d2 ) ) % 3 == 0 ){
                x = ( a - ( ( 2 * d1 ) + d2 ) ) /3;
            }
        }
        if( x == -1 )
        return x;
        if( x < 0 || ( x + d1 ) < 0 || ( x + d1 + d2 ) < 0 )
        return -1;
        if( ( b - x ) >= 0 ){
            ans += ( b - x );
        }
        else{
            return -1;
        }
        if( b - ( x + d1 ) >= 0 ){
            ans += ( b - ( x + d1 ) );
        }
        else{
            return -1;
        }
        if( b - ( x + d1 + d2 ) >= 0 ){
            ans += ( b - ( x + d1 + d2 ) );
        }
        else
        return -1;
        return ans;
    }
    public static long second( long d1, long d2, long a, long b ){
        long ans = 0;long x = -1;
        if( ( a - ( ( 2 * d1 ) - d2 ) ) > -1 ){
            if( ( a - ( ( 2 * d1 ) - d2 ) ) % 3 == 0 ){
                x = ( a - ( ( 2 * d1 ) - d2 ) ) /3;
            }
        }
        if( x == -1 )
        return x;
        if( x < 0 || ( x + d1 ) < 0 || ( x + d1 - d2 ) < 0 )
        return -1;
        if( ( b - x ) >= 0 ){
            ans += ( b - x );
        }
        else{
            return -1;
        }
        if( b - ( x + d1 ) >= 0 ){
            ans += ( b - ( x + d1 ) );
        }
        else{
            return -1;
        }
        if( b - ( x + d1 - d2 ) >= 0 ){
            ans += ( b - ( x + d1 - d2 ) );
        }
        else
        return -1;
        return ans;
    }
    public static long third( long d1, long d2, long a, long b ){
        long ans = 0;long x = -1;
        if( ( a - ( ( -2 * d1 ) + d2 ) ) > -1 ){
            if( ( a - ( ( -2 * d1 ) + d2 ) ) % 3 == 0 ){
                x = ( a - ( ( -2 * d1 ) + d2 ) ) /3;
            }
        }
        if( x == -1 )
        return x;
        if( x < 0 || ( x - d1 ) < 0 || ( x - d1 + d2 ) < 0 )
        return -1;
        if( ( b - x ) >= 0 ){
            ans += ( b - x );
        }
        else{
            return -1;
        }
        if( b - ( x - d1 ) >= 0 ){
            ans += ( b - ( x - d1 ) );
        }
        else{
            return -1;
        }
        if( b - ( x - d1 + d2 ) >= 0 ){
            ans += ( b - ( x - d1 + d2 ) );
        }
        else
        return -1;
        return ans;
    }
    public static long fourth( long d1, long d2, long a, long b ){
        long ans = 0;long x = -1;
        if( ( a - ( ( -2 * d1 ) - d2 ) ) > -1 ){
            if( ( a - ( ( -2 * d1 ) - d2 ) ) % 3 == 0 ){
                x = ( a - ( ( -2 * d1 ) - d2 ) ) /3;
            }
        }
        if( x == -1 )
        return x;
        if( x < 0 || ( x - d1 ) < 0 || ( x - d1 - d2 ) < 0 )
        return -1;
        if( ( b - x ) >= 0 ){
            ans += ( b - x );
        }
        else{
            return -1;
        }
        if( b - ( x - d1 ) >= 0 ){
            ans += ( b - ( x - d1 ) );
        }
        else{
            return -1;
        }
        if( b - ( x - d1 - d2 ) >= 0 ){
            ans += ( b - ( x - d1 - d2 ) );
        }
        else
        return -1;
        return ans;
    }
    public static void main (String[] args) throws java.lang.Exception
    {
        Reader sn = new Reader();
        Print p = new Print();
        int t = sn.nextInt();
        while( t -- > 0 ){
            int ans = 0;
            long n = sn.nextLong();
            long k = sn.nextLong();
            long d1 = sn.nextLong();
            long d2 = sn.nextLong();
            if( ( n % 3 ) == 0){
                if( first( d1, d2, k, n/3 ) != -1 ){
                    long a = first( d1, d2, k, n/3 );
                    if( ( ( n - k ) - a ) > -1 ){
                        ans = 1;
                    }
                }
                if( second( d1, d2, k, n/3 ) != -1 ){
                    long a = second( d1, d2, k, n/3 );
                    if( ( ( n - k ) - a ) > -1 ){
                        ans = 1;
                    }
                }
                if( third( d1, d2, k, n/3 ) != -1 ){
                    long a = third( d1, d2, k, n/3 );
                    if( ( ( n - k ) - a ) > -1 ){
                        ans = 1;
                    }
                }
                if( fourth( d1, d2, k, n/3 ) != -1 ){
                    long a = fourth( d1, d2, k, n/3 );
                    if( ( ( n - k ) - a ) > -1 ){
                       ans = 1;
                    }}
                    if( ans == 1 )
                    p.printLine("yes");
                    else
                    p.printLine("no");
                
            }
            else{
                p.printLine("no");
            }
        }
      p.close();
    }
}
class Pair implements Comparable<Pair> {
		int val;
		int in;
		Pair(int a, int b){
			val=a;
	        in=b;
		}
		@Override
		public int compareTo(Pair o) {
			if(val==o.val)
			return Integer.compare(in,o.in);
			else
			return Integer.compare(val,o.val);
		}}
class Reader
    {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;
        public boolean isSpaceChar(int c) { return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1; }
        public Reader()
        {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public Reader(String file_name) throws IOException
        {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }
 
        public String readLine() throws IOException
        {
            byte[] buf = new byte[64]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1)
            {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }
        
        public String readWord()throws IOException
        {
		int c = read();
		while (isSpaceChar(c)) c = read();        
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		}while (!isSpaceChar(c));
		return res.toString();
	    } 
	
        public int nextInt() throws IOException
        {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do
            {
                ret = ret * 10 + c - '0';
            }  while ((c = read()) >= '0' && c <= '9');
 
            if (neg)
                return -ret;
            return ret;
        }
 
        public long nextLong() throws IOException
        {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }
 
        public double nextDouble() throws IOException
        {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
 
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
 
            if (c == '.')
            {
                while ((c = read()) >= '0' && c <= '9')
                {
                    ret += (c - '0') / (div *= 10);
                }
            }
 
            if (neg)
                return -ret;
            return ret;
        }
 
        private void fillBuffer() throws IOException
        {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }
 
        private byte read() throws IOException
        {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }
 
        public void close() throws IOException
        {
            if (din == null)
                return;
            din.close();
        }
    }
class Print
{
    private final BufferedWriter bw;
    public Print()
    {
        bw=new BufferedWriter(new OutputStreamWriter(System.out));
    }
    public void print(String str)throws IOException
    {
        bw.append(str);
    }
    public void printLine(String str)throws IOException
    {
        print(str);
        bw.append("\n");
    }
    public void close()throws IOException
    {
        bw.close();
    }}