You suspect that the pyramids were built by aliens. A pyramid is a structure consisting of n layers of stones such that the i\text{th} layer of stones from the top has i stones in it. You observe that the quality of the building materials increases the higher the stones are, with the topmost stone having quality q. If aliens had built the pyramids, you believe that the qualities of the stones would be positive integers such that the quality of a stone is exactly the sum of the qualities of the two stones below it. Can you find the qualities of the stones in the bottom layer of a given pyramid to prove that aliens built them?

Input

The only line of the input has two integers n and q.

Output

Print any valid way to choose the stone qualities in the bottom layer. If there are no solutions, print "The truth is out there".

Constraints

• 1 \le n \le 60
• 1 \le q \le 10^{18}

Example 1

Input:

3 8

Output:

2 1 4

Explanation: the qualities of the stones are

  8
 3 5
2 1 4

Example 2

Input:

2 1

Output:

The truth is out there