Lucky Permutation

Description:

Input:

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.

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.

Sample Input:

7 4

Sample Output:

1

Sample Input:

4 7

Sample 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.