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
range = xrange
input = raw_input

MOD = 10**9 + 7

big = 2 * 10**5 + 100
DP = [[-1] * 10 for _ in range(big)]

DP[0] = [1] * 10
for i in range(1, big):
    DPi = DP[i]
    DPim1 = DP[i - 1]

    DPi[0] = DPim1[1]
    DPi[1] = DPim1[2]
    DPi[2] = DPim1[3]
    DPi[3] = DPim1[4]
    DPi[4] = DPim1[5]
    DPi[5] = DPim1[6]
    DPi[6] = DPim1[7]
    DPi[7] = DPim1[8]
    DPi[8] = DPim1[9]
    DPi[9] = (DPim1[1] + DPim1[0]) % MOD


inp = [int(x) for x in sys.stdin.read().split()]; ii = 0
out = []

t = inp[ii]; ii += 1
for _ in range(t):
    n = inp[ii]; ii += 1
    m = inp[ii]; ii += 1

    ans = sum(DP[m][int(c)] for c in str(n)) % MOD
    out.append(ans)

print '\n'.join(str(x) for x in out)
