There is a chessboard with $n$ rows and $m$ columns, containing a total of $nm$ cells. Please place chess pieces in the cells (each cell can contain at most one piece) such that for all $1 \le i \le m$, the $i$-th column contains exactly $a_i$ pieces. Additionally, no two pieces on the board can be adjacent (sharing an edge).

Determine if a valid configuration exists. If it exists, output any one valid configuration.

Input

Read the data from standard input.

The first line contains two positive integers $n, m$, where $n \le 300$ and $m \le 300$.

The second line contains $m$ non-negative integers $a_1, a_2, \dots, a_m$, where $0 \le a_i \le n$.

Output

Output to standard output.

If no solution exists, output the string No.

If a solution exists, output the string Yes on the first line, followed by $n$ lines, each containing a string of length $m$, representing your constructed board configuration. Here, 0 represents an empty cell, and 1 represents a cell containing a piece.

Examples

Input 1

3 4
2 1 2 1

Output 1

Yes
1010
0101
1010

Input 2

3 4
2 3 3 3

Output 2

No