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.

Input

The first line contains a single integer t (1 ≤ t ≤ 2 ⋅ 10^5) — the number of test cases.

The only line of each test case contains two integers n (1 ≤ n ≤ 10^9) and m (1 ≤ m ≤ 2 ⋅ 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.

Example

Input


5
1912 1
5 6
999 1
88 2
12 100


Output


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.
//   package com.anesthesia.analyze;

import java.io.*;
import java.util.*;

public class Main {
    static int[] dp = new int[2*(int)1e5 + 10];
    static int mod = (int)1e9 + 7;
    public static void main(String[] args) throws IOException {
        for(int i= 0;i<dp.length;i++){
            if(i < 10)
                dp[i] = 1;
            else
                dp[i] = (dp[i-10]+dp[i-9])%mod;
        }
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        BufferedWriter log = new BufferedWriter(new OutputStreamWriter(System.out));
        int T = Integer.valueOf(reader.readLine());
        while(T -- != 0) {
            String[] str = reader.readLine().split(" ");
            int n = Integer.valueOf(str[0]), k = Integer.valueOf(str[1]);
            int res = 0;
            while(n != 0) {
                res = (dp[n%10 + k] + res) % mod;
                n /= 10;
            }
            log.write(res + "\n");
            log.flush();
        }


    }
}