Sequence

Limits: 2 sec., 256 MiB

This statement was translated automatically from Ukrainian.

Marichka really loves lucky digital sequences, and Zenyk is ready to get any such sequence for her. So, Marichka’s requirements for a lucky sequence are as follows:

1. The sequence consists of the digits 4 and 7.

2. The length of the sequence is \(n\).

3. Two fours do not appear consecutively in the sequence.

4. The sequence is at the \(k\)-th position in the lexicographically sorted list of all possible sequences.

You need to help Zenyk determine this sequence.

Input

The single line contains two positive integers \(n\) and \(k\) — the length of the sequence and the position in the sorted list of all possible sequences, respectively.

Output

In the single line, print the \(k\)-th lucky sequence, or Flowers if \(k\) is greater than their total number.

Constraints

\(1 \le n \le 80\),

\(1 \le k \le 10^{18}\).

Samples

Input (stdin) сopy	Output (stdout) сopy
4 7	7774

Input (stdin) сopy	Output (stdout) сopy
3 10	Flowers

Notes

Sorted list of sequences of length 4 and 3 respectively:

4747, 4774, 4777, 7474, 7477, 7747, 7774, 7777.

474, 477, 747, 774, 777.