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.util.*;
import java.io.*;

public class Rextester {
    static final FS sc          = new FS();
    static final PrintWriter pw = new PrintWriter(System.out);
    static final Util u         = new Util();
    
    public static void main(String[] args) {
        int testCases = sc.nextInt();
        while(testCases-- > 0) {
            int n = sc.nextInt(), m = sc.nextInt(), a = sc.nextInt(), b = sc.nextInt();
            if(n*a != m*b) {
                pw.println("NO");
            } else {
                pw.println("YES");
                int[][] r = new int[n][m];
                int start = 0;
                for(int i = 0; i<n; i++) {
                    int ptr = 0;
                    while(ptr < a){
                        r[i][(start+ptr++)%m] = 1;
                    }
                    start += a;
                }
                for(int i = 0; i<n; i++) { for(int j = 0; j<m; j++) pw.print(r[i][j]); pw.println(); }
            }
        }
        pw.flush();
    }
    
    

    static class FS {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer("");
        String next() {
            while(!st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch(Exception e) {}
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }
        
    static class Util {
        
        void sc1D(int[] a) {
            for(int i = 0; i<a.length; i++)
                    a[i] = sc.nextInt();
        }

        void sc2D(int[][] a) {
            for(int i = 0; i<a.length; i++)
                for(int j = 0; j<a[0].length; j++)
                        a[i][j] = sc.nextInt();
        }
        
        int gcd(int number1, int number2) {
            if (number2 == 0)
                return number1;
            return gcd(number2, number1 % number2);
        }
        
    }
    
}