Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C. Lucky Subsequence

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya 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).

Input

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*.

Output

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

Examples

Input

3 2

10 10 10

Output

3

Input

4 2

4 4 7 7

Output

4

Note

In the first sample all 3 subsequences of the needed length are considered lucky.

In the second sample there are 4 lucky subsequences. For them the sets of indexes equal (the indexation starts from 1): {1, 3}, {1, 4}, {2, 3} and {2, 4}.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Feb/16/2019 13:42:43 (d3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|