A8344. Lucky Permutation

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

One day Petya dreamt of a lexicographically $k$ -th permutation of integers from $1$ to $n$ . Determine how many lucky numbers in the permutation are located on the positions whose indexes are also lucky numbers.

The first line contains two integers $n$ and $k$ $(1<=n,k<=10^{9})$ — the number of elements in the permutation and the lexicographical number of the permutation.

If the $k$ -th permutation of numbers from $1$ to $n$ does not exist, print the single number "-1" (without the quotes). Otherwise, print the answer to the problem: the number of such indexes $i$ , that $i$ and $a_{i}$ are both lucky numbers.

A permutation is an ordered set of $n$ elements, where each integer from $1$ to $n$ occurs exactly once. The element of permutation in position with index $i$ is denoted as $a_{i}$ ( $1<=i<=n$ ). Permutation $a$ is lexicographically smaller that permutation $b$ if there is such a $i$ ( $1<=i<=n$ ), that $a_{i}<b_{i}$ , and for any $j$ ( $1<=j<i$ ) $a_{j}=b_{j}$ . Let's make a list of all possible permutations of $n$ elements and sort it in the order of lexicographical increasing. Then the lexicographically $k$ -th permutation is the $k$ -th element of this list of permutations.

In the first sample the permutation looks like that:

1 2 3 4 6 7 5

The only suitable position is 4.

In the second sample the permutation looks like that:

2 1 3 4

The only suitable position is 4.