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.
#   Author: yumtam
#   Created at: 2021-04-29 12:58

MOD = 10**9 + 7

a = []
c = [1] + [0]*9

for _ in range(2 * 10**5 + 50):
    a.append(sum(c))
    d = [0] * 10
    for i in range(9):
        d[i+1] = c[i]
    d[0] = (d[0] + c[9]) % MOD
    d[1] = (d[1] + c[9]) % MOD
    c = d

import sys, os, io
input = lambda: sys.stdin.readline().rstrip('\r\n')
stdout = io.BytesIO()
sys.stdout.write = lambda s: stdout.write(s.encode("ascii"))

for _ in range(int(input())):
    n, k = [int(t) for t in input().split()]

    s = str(n)
    c = [s.count(str(i)) for i in range(10)]

    ans = 0
    for i in range(10):
        ans = (ans + c[i] * a[i+k]) % MOD

    print(ans)

os.write(1, stdout.getvalue())
