Codeforces 327C 乘法逆元 + 费马小定理 || 等比数列二分求和取模

C. Magic Five

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

There is a long plate s containingn 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 by5. Note that, the resulting number may contain leading zeros.

Now Iahub wants to count the number of ways he can obtain magic number, modulo1000000007 (10⁹ + 7). Two ways are different, if the set of deleted positions ins 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 integerk (1 ≤ k ≤ 10⁹). The plates is formed by concatenating k copies of a together. That isn = |a|·k.

Output

Print a single integer — the required number of ways modulo1000000007 (10⁹ + 7).

Examples

Input

1256
1

Output