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.
#include <iostream>
#include <vector>
#include <map>

using namespace std;

const int MAX_N = 2e5 + 5, MOD = 1e9 + 7;
int length[MAX_N];

void precompute()
{
    for(int i = 0; i <= 8; i++)
    {
        length[i] = 2;
    }

    length[9] = 3;

    for(int i = 10; i < MAX_N; i++)
    {
        length[i] = (length[i - 9] + length[i - 10])%MOD;
    }
}

void solve()
{
    int n, no_of_operations;
    cin >> n >> no_of_operations;

    long long answer = 0;
    while(n > 0)
    {
        int digit = n%10;

        long long this_length = (no_of_operations < 10 - digit ? 1 : length[no_of_operations - (10 - digit)]);

        //cout << "D = " << digit << " this = " << this_length << "\n";

        n /= 10;

        answer = (answer + this_length)%MOD;
    }

    cout << answer << "\n";
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(NULL);
    precompute();

    int no_of_test_cases;
    cin >> no_of_test_cases;

    while(no_of_test_cases--)
        solve();

    return 0;
}


