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.

Input

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 $*n* = |*a*|·*k*$.

Output

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

Note

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.