You are given four positive integers n, m, a, b (1 ≤ b ≤ n ≤ 50; 1 ≤ a ≤ m ≤ 50). Find any such rectangular matrix of size n × m that satisfies all of the following conditions:

  * each row of the matrix contains exactly a ones; 
  * each column of the matrix contains exactly b ones; 
  * all other elements are zeros. 



If the desired matrix does not exist, indicate this.

For example, for n=3, m=6, a=2, b=1, there exists a matrix satisfying the conditions above:

$$$ \begin{vmatrix} 0 & 1 & 0 & 0 & 0 & 1 \\\ 1 & 0 & 0 & 1 & 0 & 0 \\\ 0 & 0 & 1 & 0 & 1 & 0 \end{vmatrix} $$$

Input

The first line contains an integer t (1 ≤ t ≤ 1000) — the number of test cases. Then t test cases follow.

Each test case is described by four positive integers n, m, a, b (1 ≤ b ≤ n ≤ 50; 1 ≤ a ≤ m ≤ 50), where n and m are the sizes of the matrix, and a and b are the number of ones for rows and columns, respectively.

Output

For each test case print:

  * "YES" (without quotes) and the required matrix (if there are several answers, print any) if it exists, or 
  * "NO" (without quotes) if it does not exist. 



To print the matrix n × m, print n rows, each of which consists of m numbers 0 or 1 describing a row of the matrix. Numbers must be printed without spaces.

Example

Input


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


Output


YES
010001
100100
001010
NO
YES
11
11
YES
1100
1100
0011
0011
YES
1
1
/*==========================================================================
*   	AUTHOR:    RonWonWon
*   	CREATED:   10.06.2021 04:22:59        
/*==========================================================================*/
import java.io.*;
import java.util.*;

public class G {
	
	public static void main(String[] args) throws IOException {
		/*
    in.ini();
    PrintWriter out = new PrintWriter(new BufferedWriter(new FileWriter("output.txt")));
    */
    long startTime = System.nanoTime();
    int t = in.nextInt(), T = 1;  
    while(t-->0) { 
    	int n = in.nextInt(), m = in.nextInt(), a = in.nextInt(), b = in.nextInt();
    	Pair id[] = new Pair[m];
    	for(int i=0;i<m;i++) id[i] = new Pair(i,0);
    	int ans[][] = new int[n][m];
    	for(int i=0;i<n;i++){
				Arrays.sort(id);
				for(int j=0;j<a;j++){
					ans[i][id[j].x] = 1;
					id[j].y++;
				}	
    	}  
    	int col[] = new int[m];
    	for(int i=0;i<m;i++){
    		for(int j=0;j<n;j++) col[i] += ans[j][i];
    	}
    	boolean allSame = true;
    	for(int i=0;i<m-1;i++) if(col[i]!=col[i+1]) allSame = false;
    	if(allSame&&col[0]==b){
    		out.println("YES");
    		for(int i=0;i<n;i++){
    			for(int j=0;j<m;j++) out.print(ans[i][j]);
    			out.println();
    		}
    	}
    	else out.println("NO");
   		//out.println("Case #"+T+": "+ans); T++;
    }
    /*
    startTime = System.nanoTime() - startTime;
    System.err.println("Time: "+(startTime/1000000));
    */
    out.flush();
	}
	
	static class Pair implements Comparable<Pair> {
		int x, y;
		Pair(int a, int b){ x = a; y = b; }		
		@Override
		public int compareTo(Pair o) {
			if(o.y - this.y>0)
				return -1;
			else if(o.y - this.y<0)
				return 1;
			else 
				return 0;
		}
	}
	
	static FastScanner in = new FastScanner();
  static PrintWriter out = new PrintWriter(System.out);
	static int oo = Integer.MAX_VALUE;
	
	static class FastScanner {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer("");
		
		void ini() throws FileNotFoundException {
			br = new BufferedReader(new FileReader("input.txt"));
		}
		
		String next() {
			while(!st.hasMoreTokens())
				try { st = new StringTokenizer(br.readLine()); }
				catch(IOException e) {}
			return st.nextToken();
		}
		
		String nextLine(){
			try{ return br.readLine(); } 
			catch(IOException e) { } return "";
		}
		
		int nextInt() {
			return Integer.parseInt(next());
		}
		
		int[] readArray(int n) {
			int a[] = new int[n];
			for(int i=0;i<n;i++) a[i] = nextInt();
			return a;
		}
		
		long nextLong() {
			return Long.parseLong(next());
		}
		
		long[] readArrayL(int n) {
			long a[] = new long[n];
			for(int i=0;i<n;i++) a[i] = nextLong();
			return a;
		}
		
		double nextDouble() {
			return Double.parseDouble(next());
		}
		
		double[] readArrayD(int n) {
			double a[] = new double[n];
			for(int i=0;i<n;i++) a[i] = nextDouble();
			return a;
		}
	}

	static final Random random = new Random();

	static void ruffleSort(int[] a){
		int n = a.length;
		for(int i=0;i<n;i++){
			int j = random.nextInt(n), temp = a[j];
			a[j] = a[i]; a[i] = temp;
		}
		Arrays.sort(a); 	
	}
	
	static void ruffleSortL(long[] a){
		int n = a.length;
		for(int i=0;i<n;i++){
			int j = random.nextInt(n);
			long temp = a[j];
			a[j] = a[i]; a[i] = temp;
		}
		Arrays.sort(a); 	
	}
}
