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.BufferedReader;
import java.io.InputStreamReader;

public class AddOne {
    public static void main(String[] args) throws Exception {
        BufferedReader buffer = new BufferedReader(new InputStreamReader(System.in));
        StringBuilder sb = new StringBuilder();
        int [][] dp = new int[2_00_001][10];
        int MOD = 1_000_000_007;
        for (int i = 0; i < 10; i++)
            dp[0][i] = 1;
        for (int i = 1; i < 2_00_001; i++) {
            for (int j = 0; j < 9; j++) {
                dp[i][j] = dp[i-1][j+1];
            }
            dp[i][9] = (dp[i-1][0] + dp[i-1][1])%MOD;
        }
        int t = Integer.parseInt(buffer.readLine());
        while (t-- > 0) {
            String [] inp = buffer.readLine().split(" ");
            char [] num = inp[0].toCharArray();
            int steps = Integer.parseInt(inp[1]);
            long ans = 0;
            for (char ch : num) {
                ans += dp[steps][ch-'0'];
                ans %= MOD;
            }
            sb.append(ans).append("\n");
        }
        System.out.println(sb);
    }
}
