Searching an Array

Your friend has a sorted array of $n$ integers, and he wants you to find whether it contains a number $k$. You can make a maximum of $\lceil \log_2(n) \rceil$ queries of the following form:

• What is the number at the $x$-th position? (1 indexed).

Interaction

The first line of input contains two integers, $n$ and $k$.

To query the number at the $x$-th position, print a line containing only $x$ and the judge will respond with the number $(\le 10^{18})$ at that position, which you can read as a line of input.

To give a final answer, print "YES" or "NO", answering whether the integer exists in the array.

Constraints

• $1 \le n \le 10^9$
• $1 \le k \le 10^{18}$