A8455 | Lucky Subsequence

Petya loves lucky numbers very much. Everybody knows that lucky numbers are positive integers whose decimal record contains only the lucky digits 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.

Petya has sequence $a$ consisting of $n$ integers.

The subsequence of the sequence $a$ is such subsequence that can be obtained from $a$ by removing zero or more of its elements.

Two sequences are considered different if index sets of numbers included in them are different. That is, the values ​of the elements ​do not matter in the comparison of subsequences. In particular, any sequence of length $n$ has exactly $2^{n}$ different subsequences (including an empty subsequence).

A subsequence is considered lucky if it has a length exactly $k$ and does not contain two identical lucky numbers (unlucky numbers can be repeated any number of times).

Help Petya find the number of different lucky subsequences of the sequence $a$ . As Petya's parents don't let him play with large numbers, you should print the result modulo prime number $1000000007$ $(10^{9}+7)$ .

The first line contains two integers $n$ and $k$ $(1<=k<=n<=10^{5})$ . The next line contains $n$ integers $a_{i}$ ( $1<=a_{i}<=10^{9}$ ) — the sequence $a$ .

On the single line print the single number — the answer to the problem modulo prime number $1000000007$ $(10^{9}+7)$ .