+/- Rectangle

You are given four integers: H, W, h and w (1 ≤ h ≤ H, 1 ≤ w ≤ W). Determine whether there exists a matrix such that all of the following conditions are held, and construct one such matrix if the answer is positive:

• The matrix has H rows and W columns.
• Each element of the matrix is an integer between -10^9 and 10^9 (inclusive).
• The sum of all the elements of the matrix is positive.
• The sum of all the elements within every subrectangle with h rows and w columns in the matrix is negative.

Constraints

• 1 ≤ h ≤ H ≤ 500
• 1 ≤ w ≤ W ≤ 500

Input

Input is given from Standard Input in the following format:

H W h w

Output

If there does not exist a matrix that satisfies all of the conditions, print No.

Otherwise, print Yes in the first line, and print a matrix in the subsequent lines in the following format:

a_{11} ... a_{1W} : a_{H1} ... a_{HW}

Here, a_{ij} represents the (i,\ j) element of the matrix.

Examples

Input

3 3 2 2

Output

Yes 1 1 1 1 -4 1 1 1 1

Input

2 4 1 2

Output

No

Input

3 4 2 3

Output

Yes 2 -5 8 7 3 -5 -4 -5 2 1 -1 7

inputFormat

Input

Input is given from Standard Input in the following format:

H W h w

outputFormat

Output

If there does not exist a matrix that satisfies all of the conditions, print No.

Otherwise, print Yes in the first line, and print a matrix in the subsequent lines in the following format:

a_{11} ... a_{1W} : a_{H1} ... a_{HW}

Here, a_{ij} represents the (i,\ j) element of the matrix.

Examples

Input

3 3 2 2

Output

Yes 1 1 1 1 -4 1 1 1 1

Input

2 4 1 2

Output

No

Input

3 4 2 3

Output

Yes 2 -5 8 7 3 -5 -4 -5 2 1 -1 7

样例

2 4 1 2

No