Say we have a square that has W cells on each side and, therefore, W² cells total. Let's go further and fill each cell with one of the following:</p>

• A digit from 0 to 9;
• The addition sign (+);
• The subtraction sign (-).

If, finally, we add a constraint that no 2 digits are horizontally or vertically adjacent and no 2 operators (+ or -) are horizontally or vertically adjacent, then our square can be called an "arithmetic square".

Square Math is the name of a puzzle where, given an arithmetic square, we start from any numeric cell and move either horizontally or vertically a cell at a time, finally ending in a numerical cell. The mathematical expression we get from the traversal is evaluated to get a single value. For example:

2+3
+4-
1+0

The above is a valid arithmetic square of size W = 3. If we start from "2", move horizontally right, then vertically down, we'll get "2+4", which gives a value of "6". If we further move horizontally right, then vertically up, we'll get "2+4-3", which is equal to "3".

In Square Math, there is no limit to how many times you can use a particular cell. It is perfectly legal to move from a cell to its neighbor, then back to the original cell. Given an arithmetic square and a list of queries, your task is to find a Square Math expression which evaluates to each query.

입력 형식

The first line of input contains a single integer, T. T test cases follow. The first line of each test case contains 2 integers, W and Q. W lines follow, each containing W characters, representing the arithmetic square. Don't worry, all arithmetic squares in the input are well-formed. The following line contains a space separated list of Q integers, representing the values which need to be computed by using Square Math (the queries). You can assume that all given values will have at least one possible Square Math solution.</p>

Limits

• 1 ≤ T ≤ 60
• 2 ≤ W ≤ 20
• 1 ≤ Q ≤ 50
• 1 ≤ each query ≤ 250

For each test case, begin output with "Case #X:" on a line by itself, where X is the test case number, starting from 1. Then, for each query within the test case, print the Square Math expression which evaluates to the query on a line by itself.

In the case where there are multiple possible Square Math expressions, print the one that is shortest. If there is still a tie, print the lexicographically smallest expression. Remember that '+' is lexicographically smaller than '-'.

예제 입력

2
5 3
2+1-2
+3-4+
5+2+1
-4-0-
9+5+1
20 30 40
3 2
2+1
+4+
5+1
2 20

예제 출력

Case #1:
1+5+5+9
3+4+5+9+9
4+9+9+9+9
Case #2:
2
5+5+5+5