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.
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main
{
    public static void main(String[] args)
    {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        TaskC solver = new TaskC();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskC
    {
        public void solve(int testNumber, Scanner in, PrintWriter out)
        {
            int T = 1;
            while (T-- > 0)
            {
                solveOne(in, out);
            }
        }

        private void solveOne(Scanner in, PrintWriter out)
        {
            int MOD = 1_000_000_000 + 7;
            int dp[][] = new int[200000 + 10][10];
            for (int i = 0; i < 10; i++) dp[0][i] = 1;
            for (int i = 1; i <= 200000 + 5; i++)
            {
                for (int j = 0; j < 9; j++)
                {
                    dp[i][j] = dp[i - 1][j + 1];
                }
                dp[i][9] = (dp[i - 1][1] + dp[i - 1][0]) % MOD;
            }
            int testCases = in.nextInt();
            while (testCases-- > 0)
            {
                int N = in.nextInt();
                int M = in.nextInt();
                String s = "" + N;
                int ans = 0;
                for (char c : s.toCharArray())
                {
                    ans = (ans + dp[M][c - '0']) % MOD;
                }
                out.println(ans);
            }
        }

    }
}

