1513_C. Add One
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.
```python
from os import path
import sys,time
from math import ceil, floor,gcd,log,log2 ,factorial
from collections import defaultdict ,Counter , OrderedDict , deque
from heapq import heapify , heappush , heappop
from bisect import *
# from functools import reduce
from operator import mul
from itertools import permutations
maxx, mod  = float('inf') , int(1e9 + 7)
localsys ,start_time = 0 , time.time()
if (path.exists('input.txt')):
    localsys = 1;sys.stdin=open('input.txt','r');sys.stdout=open('output.txt','w');
#left shift --- num*(2**k) --(k - shift)
input = sys.stdin.readline
N = int(2e5 + 10)
dp =[1]*N
for i in range(10 , N):
    dp[i] = (dp[i-9] + dp[i-10])%mod
for _ in range(int(input())):
    n , m = map(int , input().split()) ; ans =0
    while n :
        i = n%10 ; n//=10
        ans = (ans + dp[i + m])%mod
    print(ans)



    






if localsys:
    print("\n\n\nTime Elased :",time.time() - start_time,"seconds")
```