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,functools,collections,bisect,math,heapq
input = sys.stdin.readline
#print = sys.stdout.write  
mod = 10**9 + 7
sys.setrecursionlimit(300000)

N = 200001
dp = [0]*N
for i in range(9):
    dp[i] = 2
dp[9] = 3
for i in range(10,N):
    dp[i] = dp[i-9]+dp[i-10]
    dp[i] %= mod 

t = int(input())    
for _ in range(t):
    s,m = input().strip().split()
    m = int(m)
    s = list(map(int,list(s)))
    ans = 0
    for i in s:
        if m-10+i >= 0:
            ans += dp[m-10+i]
        else:
            ans += 1
    ans %= mod
    print(ans)