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 sys
input = sys.stdin.readline
t = int(input().strip())

M = 1000000007
dp = [0] * (2 * 100000+20)
dp[:10] = list(1 for i in range(10))
for i in range(10, 2*100000+20):
    dp[i] = dp[i-9] + dp[i-10]
    dp[i] %= M
while t:
    t -= 1
    n, m = map(int, input().strip().split())
    n = str(n)
    result = 0
    for i in n:
        result += dp[int(i)+m]
        result %= M
    print(result)
