CF121C.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.

Petya 喜欢幸运数字。众所周知，幸运数字是指十进制表示中仅包含幸运数字 4 和 7 的正整数。例如，47、744、4 是幸运数字，而 5、17、467 不是。

有一天，Petya 梦到了整数 $1$ 到 $n$ 的字典序第 $k$ 个排列。请确定该排列中有多少个幸运数字位于下标（位置索引）本身也是幸运数字的位置上。

The first line contains two integers n and k (1 ≤ n, k ≤ 109) — the number of elements in the permutation and the lexicographical number of the permutation.

第一行包含两个整数 $n$ 和 $k$（$1 \leq n, k \leq 10^9$）—— 分别表示排列的元素个数以及该排列的字典序编号。

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.

如果 $1$ 到 $n$ 的第 $k$ 个排列不存在，则输出单个数字 “-1”（不带引号）。否则，输出本题的答案：满足下标 $i$ 和对应元素 $a_i$ 均为幸运数的下标 $i$ 的个数。

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.

排列是 $ n $ 个元素的有序集合，其中从 $ 1 $ 到 $ n $ 的每个整数恰好出现一次。排列中索引为 $ i $（$ 1 \leq i \leq n $）位置上的元素记为 $ a_i $。若存在某个 $ i $（$ 1 \leq i \leq n $），使得 $ a_i < b_i $，且对任意 $ j $（$ 1 \leq j < i $）均有 $ a_j = b_j $，则称排列 $ a $ 在字典序上小于排列 $ b $。我们列出所有 $ n $ 个元素的可能排列，并按字典序升序排序。那么字典序第 $ k $ 小的排列即为该排列列表中的第 $ k $ 个元素。

在第一个样例中，排列如下所示：

1 2 3 4 6 7 5

唯一满足条件的位置是 4。

在第二个样例中，排列如下所示：

2 1 3 4

唯一满足条件的位置是 4。