Add One
Description
You are given an integer $n$. You have to apply $m$ operations to it.
In a single operation, you must replace every digit $d$ of the number with the decimal representation of integer $d + 1$. For example, $1912$ becomes $21023$ after applying the operation once.
You have to find the length of $n$ after applying $m$ operations. Since the answer can be very large, print it modulo $10^9+7$.
The first line contains a single integer $t$ ($1 \le t \le 2 \cdot 10^5$) — the number of test cases.
The only line of each test case contains two integers $n$ ($1 \le n \le 10^9$) and $m$ ($1 \le m \le 2 \cdot 10^5$) — the initial number and the number of operations.
For each test case output the length of the resulting number modulo $10^9+7$.
Input
The first line contains a single integer $t$ ($1 \le t \le 2 \cdot 10^5$) — the number of test cases.
The only line of each test case contains two integers $n$ ($1 \le n \le 10^9$) and $m$ ($1 \le m \le 2 \cdot 10^5$) — the initial number and the number of operations.
Output
For each test case output the length of the resulting number modulo $10^9+7$.
Samples
5
1912 1
5 6
999 1
88 2
12 100
5
2
6
4
2115
Note
For the first test, $1912$ becomes $21023$ after $1$ operation which is of length $5$.
For the second test, $5$ becomes $21$ after $6$ operations which is of length $2$.
For the third test, $999$ becomes $101010$ after $1$ operation which is of length $6$.
For the fourth test, $88$ becomes $1010$ after $2$ operations which is of length $4$.