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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 2010-2023 Mike Mirzayanov

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