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.
from sys import stdin
dp=[0]*(2*10**5+1)
for i in range(9):
    dp[i]=2
dp[9]=3
for i in range(10,2*10**5+1):
    dp[i]=(dp[i-9]+dp[i-10])%(10**9+7)
for _ in range(int(input())):
    n,m=map(int,stdin.readline().split())
    n=str(n)
    a=[0]*len(n)
    ans=0
    for i in n:
        temp=int(i)+m
        if temp<10:
            ans+=1
        else:
            ans+=dp[m+int(i)-10]%(10**9+7)
    print((ans)%(10**9+7))
