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.*;
import java.util.StringTokenizer;

public class Main {
    
    static final long MOD = 1000000007;
    
    public static void main(String[] args) {
    
        var sc = new FastScanner(System.in);
        var pw = new PrintWriter(System.out);
        
        var c = new long[10][200001];
        for(int i = 0; i <= 9; i++){
            var a = new long[10];
            a[i] = 1;
            for(int j = 1; j <= 200000; j++){
                var b = new long[10];
                System.arraycopy(a, 0, b, 1, 9);
                b[0] = a[9];
                b[1] += a[9];
                for(int k = 0; k <= 9; k++){
                    b[k] %= MOD;
                    c[i][j] += b[k];
                }
                c[i][j] %= MOD;
                System.arraycopy(b, 0, a, 0, 10);
            }
        }
        
        int T = Integer.parseInt(sc.next());
        for(int t = 0; t < T; t++){
            String n = sc.next();
            int m = Integer.parseInt(sc.next());
            long ans = 0;
            for(int i = 0; i < n.length(); i++){
                int j = Integer.parseInt(n.substring(i, i+1));
                ans += c[j][m];
                ans %= MOD;
            }
            pw.println(ans);
        }
        pw.flush();
    }
    
    static class FastScanner {
        BufferedReader br;
        StringTokenizer st;
        
        public FastScanner(InputStream in) {
            br = new BufferedReader(new InputStreamReader(in));
        }
        String next(){
            while(st == null || !st.hasMoreTokens()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch(IOException e){
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
    }
}