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
input = sys.stdin.readline

mod = 10**9+7
maxx = (2*10**5)+20
from collections import Counter

ans = [1]*maxx
for i in range(10, maxx):
	ans[i] = (ans[i-9]+ans[i-10])%mod

for nt in range(int(input())):
	n, m = map(int,input().split())
	fans = 0
	n = str(n)
	for digit in n:
		# d = {}
		# for i in range(10):
		# 	d[i] = 0
		# d[int(digit)] = 1
		# for j in range(m):
		# 	new_d = {}
		# 	new_d[1] = (d[0]+d[9])%mod
		# 	new_d[0] = d[9]%mod
		# 	for i in range(2, 10):
		# 		new_d[i] = d[i-1]%mod
		# 	d = new_d
		# s = 0
		# for i in d:
		# 	s += d[i]
		fans += ans[m+int(digit)]
		fans %= mod

	# print (len(ans))
	# print (Counter(ans))
	print (fans%mod)
