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: Rohan Arora(codiinggeek)
 */
import java.io.*;
import java.util.*;

public class chad {
    static long mod = (long) Math.pow(10, 9) + 7;
    /*static boolean checkPrime(int n)
    {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
        if (n % 2 == 0 || n % 3 == 0)
            return false;

        for (int j = 5; j * j <= n; j = j + 6)
            if (n % j == 0 || n % (j + 2) == 0)
                return false;

        return true;
    }
*/
    public static void main(String[] args) {
        try {
            FastReader s = new FastReader();
            StringBuilder sb = new StringBuilder();
            int t = s.nextInt();
            while(t-->0){
                int n = s.nextInt();
                int m = s.nextInt();
                int a = s.nextInt();
                int b = s.nextInt();

                int ar[][] = new int[n][m];
                int row[] = new int[n];
                int col[] = new int[m];
                int x = 0;
                for(int i=0;i<n;i++){
                    for(int j=0;j<a;j++){
                        ar[i][x] = 1;
                        col[x]++;
                        x++;
                        x = x%m;
                        row[i]++;
                    }
                }
                int p=0;
                for(int i=0;i<n;i++){
                    if(row[i]!=a){
                        p=1;
                        break;
                    }
                }
                for(int i=0;i<m;i++){
                    if(col[i]!=b){
                        p=1;
                        break;
                    }
                }
                if(p==1){
                    sb.append("NO\n");
                }else {
                    sb.append("YES\n");
                    for (int i = 0; i < n; i++) {
                        for (int j = 0; j < m; j++) {
                            sb.append(ar[i][j]);
                        }
                        sb.append("\n");
                    }
                }
            }
            System.out.println(sb);
        } catch (Exception e) {
            System.out.println(e);
            return;
        }
    }

    /**POWER CALCULATION FOR LARGE VALUES*/
    static long expo(long b, long ex) {
        long t = 1L;
        while (ex > 0) {

            if (ex % 2 != 0)
                t = (t * b) % mod;

            b = (b * b) % mod;
            ex /= 2;
        }
        return t % mod;
    }

    /**Pair class */
    class Pair<U, V> {
        U first;
        V second;

        Pair(U a, V b) {
            first = a;
            second = b;
        }
    }
/**---------------------------------------------------------------------------------*/
    /** FAST I/O */
    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;
        }
    }
}
