G. D-Function
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

Let $$$D(n)$$$ represent the sum of digits of $$$n$$$. For how many integers $$$n$$$ where $$$10^{l} \leq n < 10^{r}$$$ satisfy $$$D(k \cdot n) = k \cdot D(n)$$$? Output the answer modulo $$$10^9+7$$$.

Input

The first line contains an integer $$$t$$$ ($$$1 \leq t \leq 10^4$$$) – the number of test cases.

Each test case contains three integers $$$l$$$, $$$r$$$, and $$$k$$$ ($$$0 \leq l < r \leq 10^9$$$, $$$1 \leq k \leq 10^9$$$).

Output

For each test case, output an integer, the answer, modulo $$$10^9 + 7$$$.

Example
Input
6
0 1 4
0 2 7
1 2 1
1 2 3
582 74663 3
0 3 1
Output
2
3
90
12
974995667
999
Note

For the first test case, the only values of $$$n$$$ that satisfy the condition are $$$1$$$ and $$$2$$$.

For the second test case, the only values of $$$n$$$ that satisfy the condition are $$$1$$$, $$$10$$$, and $$$11$$$.

For the third test case, all values of $$$n$$$ between $$$10$$$ inclusive and $$$100$$$ exclusive satisfy the condition.