Add One

题意翻译

称“将一个数上每一位的值$+1$”为一次操作，例如对于$93$进行一次操作后的结果为$104$。输入$n,m$，输出对$n$进行$m$次操作的结果。

题目描述

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 $ .

输入输出格式

输入格式

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.

输出格式

For each test case output the length of the resulting number modulo $ 10^9+7 $ .

输入输出样例

输入样例 #1

5
1912 1
5 6
999 1
88 2
12 100

输出样例 #1

5
2
6
4
2115

说明

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 $ .