Problem2058--Magic Five

2058: Magic Five

Time Limit: 1 Sec  Memory Limit: 256 MB
Submit: 2  Solved: 1
[Submit] [Status] [Web Board] [Creator:]

Description

There is a long plate s containing n digits. Iahub wants to delete some digits (possibly none, but he is not allowed to delete all the digits) to form his "magic number" on the plate, a number that is divisible by 5. Note that, the resulting number may contain leading zeros.

Now Iahub wants to count the number of ways he can obtain magic number, modulo 1000000007 (109 + 7). Two ways are different, if the set of deleted positions in s differs.

Look at the input part of the statement, s is given in a special form.

Input

In the first line you're given a string a (1 ≤ |a| ≤ 105), containing digits only. In the second line you're given an integer k (1 ≤ k ≤ 109). The plate s is formed by concatenating k copies of a together. That is n = |ak.

Output

Print a single integer — the required number of ways modulo 1000000007 (109 + 7).

Sample Input Copy

1256
1
13990
2
555
2

Sample Output Copy

4
528
63

Source/Category