Display a Connect Four game Connect Four is a game where two players take turns to drop disks into columns of a vertically mounted grid, and attempt to connect four disks orthogonally or diagonally. When a column is chosen, the disk falls to the lowest empty position in that column, so any game may be completely specified by the size of the grid and the sequence of columns chosen. The task is to generate the configuration of the grid given this information.

Input


Width w and Height h of the grid, both positive integers.
Sequence of columns c1, c2, ..., cn chosen by the players, in any reasonable format (list, array etc.); either 0-based (0 to w-1) or 1-based (1 to w) indexing can be used.


It may be assumed that all of the column numbers lie within the grid (so the sequence won't contain -3 or w+50) and that any column number appears at most h times in the sequence (so a column can't be chosen once it is full).

Note that the sequence of columns may not constitute a complete game, nor a legal game. For instance, the players could opt to continue playing even after a player has connected four disks.

Output


Any reasonable representation of the resulting state of each position in the grid, either "occupied by Player 1", "occupied by Player 2", or "empty". Player 1 always moves first.


For example, a string, array, tuple etc. with each position containing one of three symbols (ASCII character, number etc.) representing the state of that position in the grid. The grid may be transposed.

For list/tuple/array outputs, the separator cannot be one of the three representative symbols. For string outputs, trailing spaces at the end of each line are permitted, provided a space is not one of the three representative symbols. Trailing newlines at the very end are permitted.

Test cases

Here, string output is used, with X, O, . denoting "occupied by Player 1", "occupied by Player 2", "empty".

IN: Width 1 Height 1 Sequence (empty sequence)
OUT:
.

IN: Width 7 Height 6 Sequence 4 4 5 5 6 7 3 [1-based]
                              3 3 4 4 5 6 2 [0-based]
OUT:
.......
.......
.......
.......
...OO..
..XXXXO

IN: Width 5 Height 5 Sequence 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 5 5 5 5 5 [1-based]
                              0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 [0-based]
OUT:
XOXOX
OXOXO
XOXOX
OXOXO
xOXOX

IN: Width 4 Height 4 Sequence 3 3 2 4 3 2 4 2 2 3 4 4 1 1 1 1 [1-based]
                              2 2 1 3 2 1 3 1 1 2 3 3 0 0 0 0 [0-based]
OUT:
OXOO
XOXX
OOOX
XXXO

IN: Width 10 Height 10 Sequence 1 2 1 3 1 4 1 5 1 6 1 7 1 8 1 9 1 10 1 10  [1-based]
                                0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0  9 0  9  [0-based]
OUT:
X.........
X.........
X.........
X.........
X.........
X.........
X.........
X.........
X........O
XOOOOOOOOO


Shortest code in bytes wins.
Vim, 34 bytes

@wO-&lt;Esc&gt;&lt;C-V&gt;(d@hpqq&lt;C-O&gt;+D@"G+bs&lt;C-R&gt;=!@.&lt;CR&gt;&lt;Esc&gt;@qq@q

Input is width in the "w register, height in the "h register, and the 1-indexed moves in the buffer, one per line. Output is a transposed grid with - as blank, 1 as player 1, and 0 as player 2 (with a bunch of newlines at the end).

To clarify, if you want Height 6, Width 7: type qh6qqw7q before starting.


@wO-&lt;Esc&gt;&lt;C-V&gt;(d@hp: Use the height and width in the registers to make a transposed grid of -s. Note that ( is run from the last line of the grid, one above the moves. This sets up the jump list.
&lt;C-O&gt;+D@"G: The &lt;C-O&gt; uses the jump list to move back to before the last G, always to the line above the next number. @"G moves to the line number indicated by the deleted text. + not only moves the cursor, but it's the failure point; when it runs on the last line, the macro dies.
+b: This maneuver goes to the first - in the line, even if it's the first character. (f- would go to the second character if the line was still all -s.)
s&lt;C-R&gt;=!@.: Replaces a - with the last insert @., but NOTted. First time through, the previous insert of - will NOT to 1 because that's the way Vim is. After that, it will alternate between 0 and 1.


Example

Start with the moves in the buffer:

4
4
5
5
6
7
3


Make sure you're on line 1 with gg, clear "q with qqq, set up the registers for width 7, height 6 with qw7qqh6q. Then run the solution above and get the following output (with newlines at the end):

------
------
1-----
10----
10----
1-----
0-----