Fractals

Time Limit: 2 Seconds    Memory Limit: 65536 KB

Fractals are self-similar patterns. One simple example is to perform the following step on a string of dashes with length 3^k to produce similar patterns. 

 Replace the middle third of each piece of dashes with spaces. Repeat until each piece consists of a single dash.

For instance, if k is 3, we start with a string of 27 dashes:
---------------------------
Remove the middle third of the string:
---------         ---------
and remove the middle third of each piece:
---   ---         ---   ---
and again:
- -   - -          - -   - -
The process stops when each group of dashes has length 1. You must write a program to specify whether ith character in the output of the last step is “-“ or  not.

Input

There are multiple test cases in the input. Each test case is given in a line containing two numbers k (less than 30) and i (at most  3^k). The goal is to find whether i^th character in the output of the last step of the above process working on a initial string of length  3^k is “-“ or not. The input terminates with a line containing 0 0.

Output

For each test case if the i^th character in the last output is “-“ you must print “Yes”; otherwise print “No”.

Sample Input

3 6
3 7
0 0

Sample Output

No
Yes

Submit

Source: 10th Iran Nationwide Internet Contest