meepo's Blog

Jzzhu has a big rectangular chocolate bar that consists of n × m unit squares. He wants to cut this bar exactly k times. Each cut must meet the following requirements:

• each cut should be straight (horizontal or vertical);
• each cut should go along edges of unit squares (it is prohibited to divide any unit chocolate square with cut);
• each cut should go inside the whole chocolate bar, and all cuts must be distinct.

The picture below shows a possible way to cut a 5 × 6 chocolate for 5 times.

Imagine Jzzhu have made k cuts and the big chocolate is splitted into several pieces. Consider the smallest (by area) piece of the chocolate, Jzzhu wants this piece to be as large as possible. What is the maximum possible area of smallest piece he can get with exactlyk cuts? The area of a chocolate piece is the number of unit squares in it.

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 2n 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 (109 + 7).