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
// #pragma GCC optimize("Ofast")
// #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")

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

import static java.lang.Math.*;

public class Main {
    static int infi = Integer.MAX_VALUE / 2, mod = 1000000007, maxn = 3 * (int) 1e5;
    static long infl = Long.MAX_VALUE / 2;


    public static void main(String[] args) throws IOException {
        br = new BufferedReader(new InputStreamReader(System.in));
        out = new PrintWriter(System.out);
        int t = nextInt();
        for (int t123 = 0; t123 < t; t123++) {
            int n = nextInt();
            int m = nextInt();
            int a = nextInt();
            int b = nextInt();
            if (n * a != m * b) {
                out.println("NO");
                continue;
            } else {
                out.println("YES");
            }
            int[][] ans = new int[n][m];
            int x = 0;
            for (int i = 1; i < m; i++) {
                if (i * n % m == 0) {
                    x = i;
                    break;

                }
            }
            int j = 0;
            for (int i = 0; i < n; i++) {
                for (int k = 0; k < a; k++) {
                    ans[i][(j + k) % m] = 1;
                }
                j += x;
                j %= m;
            }
            for (int i = 0; i < n; i++) {
                for (int k = 0; k < m; k++) {
                    out.print(ans[i][k]);
                }
                out.println();
            }
        }
        out.close();
    }

    static BufferedReader br;
    static StringTokenizer st = new StringTokenizer("");
    static PrintWriter out;

    static String next() throws IOException {
        while (!st.hasMoreTokens()) {
            st = new StringTokenizer(br.readLine());
        }
        return st.nextToken();
    }

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

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

}

class f {
    int l, r, size;

    public f(int v, int x, int y) {
        this.l = v;
        this.r = x;
        this.size = y;
    }
}