Solve the programming task below in a Python markdown code block.
There is a strange game played in ChefLand. 

The game starts with N white balls, the i-th of which has a power of S_{i}. It is known that 0 ≤ S_{i} ≤ 9. On each level, a black ball with power K hits each of the white balls. After the collision, the power of each white ball is multiplied by K. 

However, white balls are only allowed to have single-digit power. In order to maintain this, a white ball whose power contains multiple digits splits into several white balls with single-digit power, one per digit.

For example, consider a white ball with a power of 4.
If K = 2, its resulting power is 8 and it remains a single ball.
If K = 13, its resulting power is 52, so it splits into two white balls with power 5 and 2 respectively.
If K = 27, its resulting power is 108, so it splits into three white balls with power 1, 0, and 8 respectively.

The aim of the game is to determine the number of white balls after M levels. Note that K remains the same for every level.

Please help Chef win the game. Since the answer can be large, print it modulo 10^{9} + 7.

------ Input Format ------ 

- The first line of input contains a single integer T, denoting the number of test cases. The description of T test cases follows.
- The first line of each test case contains three space-separated integers N, K, and M.
- The second line of each test case contains a string S of length N, where S_{i} is the initial power of i-th ball.

------ Output Format ------ 

For each test case, output in a single line the number of white balls at the end of the game, modulo 10^{9} + 7.

------ Constraints ------ 

$1 ≤ T ≤ 100$
$1 ≤ N ≤ 1000$
$0 ≤ K,M ≤ 10^{9}$

------ subtasks ------ 

Subtask #1 (100 points): Original constraints

----- Sample Input 1 ------ 
3
4 9 2
5418
5 63 3
40514
1 100000 100000
0
----- Sample Output 1 ------ 
14
88
1

----- explanation 1 ------ 
Test case $1$:
- Initially $S = 5418$
- After the $1^{st}$, level $S = 4536972$
- After the $2^{nd}$ level, $S = 36452754816318$

There are $14$ white balls, so the answer is $14$.

Test case $3$: After each level, $S = 0$. So, the answer is $1$.