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 Permutation

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya 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.

Input

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.

Output

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.

Examples

Input

7 4

Output

1

Input

4 7

Output

1

Note

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.

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/20/2017 20:20:54 (p1).

Desktop version, switch to mobile version.

User lists

Name |
---|