A/B Matrix

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

inputFormat

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.

outputFormat

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

样例

5
3 6 2 1
2 2 2 1
2 2 2 2
4 4 2 2
2 1 1 2

YES
110000
001100
000011
NO
YES
11
11
YES
1100
0011
1100
0011
YES
1
1

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