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.BufferedWriter;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;

public class Seventh
{
    static class Pair{
        int sum,idx;
        Pair(int s,int i){
            sum=s;
            idx=i;
        }
    }
    public static void main (String[] args) throws java.lang.Exception
    {
        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter bw=new BufferedWriter(new OutputStreamWriter(System.out));
        int t=Integer.parseInt(br.readLine());
        while(t-->0){
            String A[]=br.readLine().split(" ");
            int n,m,a,b;
            n=Integer.parseInt(A[0]);
            m=Integer.parseInt(A[1]);
            a=Integer.parseInt(A[2]);
            b=Integer.parseInt(A[3]);
            int ans[][]=new int[n][m];
            int cols_sum[]=new int[m];
            int i,j;
            if(a*n!=b*m){
                bw.write("NO\n");
                continue;
            }

            bw.write("YES\n");
            for(i=0;i<n;i++){
                ArrayList<Pair> col_pair=new ArrayList();
                for(j=0;j<m;j++){
                    if(cols_sum[j]<b) {
                        //bw.write("j: cols-sum[j]: "+j+": "+cols_sum[j]+" ");
                        Pair p = new Pair(cols_sum[j], j);
                        col_pair.add(p);
                    }
                }
                //bw.write("col_sum: "+ Arrays.toString(cols_sum)+"\n");
                Collections.sort(col_pair, new Comparator<Pair>() {
                    @Override
                    public int compare(Pair o1, Pair o2) {
                        if(o1.sum>o2.sum) return 1;
                        if(o1.sum<o2.sum) return -1;
                        return 0;
                    }
                });
                /*bw.write("Col-Pair after sort:\n");
                for(j=0;j<col_pair.size();j++){
                    bw.write(col_pair.get(j).sum+" "+col_pair.get(j).idx+"\n");
                }*/
                for(j=0;j<a;j++){
                    cols_sum[col_pair.get(j).idx]+=1;
                    ans[i][col_pair.get(j).idx]=1;
                }
            }
            for(i=0;i<n;i++){
                for(j=0;j<m;j++){
                    bw.write(ans[i][j]+"");
                }
                bw.newLine();
            }
        }
        bw.flush();
    }
}