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
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.PriorityQueue;
import java.util.Scanner;
import java.util.StringTokenizer;

public class code11 {

	public static void main(String[] args) {
		// TODO Auto-generated method stub
		FastReader scn = new FastReader();
		PrintWriter out = new PrintWriter(System.out);
//		int[] arr = new int[26];
//		for(int i=0; i<26; i++) {
//			arr[i] = (int)Math.pow(2, i+1) - 1; 
//		}
			int t = scn.nextInt();
			while(t-->0) {
				int n = scn.nextInt();
				int m = scn.nextInt();
				int a = scn.nextInt();
				int b = scn.nextInt();
				int[][] mat = new int [n][m];
				int row = 0 ;
				
				for(int i=0 ; i<m ;i++) {
					int c = b;
					
					while(c>0) {
						c--;
						mat[row][i]=1;
						row = (row+1)%n;
					}
				}
				boolean isRight = true;
				
				for(int i=0 ; i<n ;i++) {
					int s =0;
					
					for(int j = 0 ; j<m ;j++) {
						s+=mat[i][j];
					}
					if(s!=a) {
						isRight = false;
					}
				}
				if(isRight) {
					out.println("YES");
					
					for(int i=0; i<n; i++) {
						for(int j=0; j<m; j++) 
							out.print(mat[i][j]);
						out.println();
					}
				}else {
					out.println("NO");
				}
			}
			out.flush();
	}
	
	public static class Pair implements Comparable<Pair>{
		int a;
		int b;
		Pair(int x, int y){
			a= x;
			b= y;
		}
		public int compareTo(Pair p) {
			if(this.b-this.a == p.b-p.a)
				return p.a - this.a;
			return (this.b-this.a) - (p.b - p.a);
		}
	}
	
	static class FastReader {
		BufferedReader br;
		StringTokenizer st;

		public FastReader() {
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next() {
			while (st == null || !st.hasMoreElements()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (IOException e) {
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

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

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

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

		String nextLine() {
			String str = "";
			try {
				str = br.readLine();
			} catch (IOException e) {
				e.printStackTrace();
			}
			return str;
		}
	}

}
