A9147. Magic Five

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 $1000000007$ ( $10^{9}+7$ ). 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.

In the first line you're given a string $a$ ( $1<=|a|<=10^{5}$ ), containing digits only. In the second line you're given an integer $k$ ( $1<=k<=10^{9}$ ). The plate $s$ is formed by concatenating $k$ copies of $a$ together. That is $n=|a|·k$ .

Print a single integer — the required number of ways modulo $1000000007$ ( $10^{9}+7$ ).

In the first case, there are four possible ways to make a number that is divisible by 5: 5, 15, 25 and 125.

In the second case, remember to concatenate the copies of $a$ . The actual plate is 1399013990.

In the third case, except deleting all digits, any choice will do. Therefore there are $2^{6}-1=63$ possible ways to delete digits.