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.*;
import java.util.*;

public class GFG {
   public static void main(String[] args) throws IOException {
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    PrintWriter out=new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
    int t = Integer.parseInt(br.readLine().trim());
    while (t--!=0) {
      StringTokenizer st = new StringTokenizer(br.readLine().trim());
//      int n = Integer.parseInt(br.readLine().trim());
      int n = Integer.parseInt(st.nextToken());
      int m = Integer.parseInt(st.nextToken());
      int a = Integer.parseInt(st.nextToken());
      int b = Integer.parseInt(st.nextToken());
      char c[][]=new char[n][m];
      for(char e[]:c)
        Arrays.fill(e,'0');
      int cnt[]=new int[n];
      int j=0,i=0;
      for(;i<m;i++){
        int q=b;
        while(q--!=0){
          c[j][i]='1';
          int k=++cnt[j];
          if(k>a) {
            i=m;
            break;
          }
          j=(j+1)%n;
        }
      }
      for(int e:cnt){
        if(e!=a){
          i=m+1;
          break;
        }
	  }
      if(i!=m)
        out.println("NO");
      else{
        out.println("YES");
        for(char e[]:c)
          out.println(e);
      }
    }
    out.close();
  }
}