You need to answer $T$ questions. Each question consists of two integers $a, b$. Count the number of integers in the range $[a, b]$ that are divisible by $k$, and the sum of their digits is also divisible by $k$.
### Input
- The first line contains an integer $T$.
- The next $T$ lines, each containing two integers $a, b$ representing a question.
### Output
- For each question, print the number of satisfying numbers.
### Constraints
- $1 \le T \le 200$.
- $1 \le a, b \le 10^{12}$.
- $1 \le k \le 10000$.
### Example
Input:
```
1
1 1000 4
```
Output:
```
64
```