Problem Statement

You are given non-negative integers $N,M$ as input.

First, let us review the notation and terminology. We define $0^0$ as $1$. Here, an infinite sequence of integers is simply called an integer sequence.

For an integer sequence $a$ and a non-negative integer $m$, $a_m$ denotes the $m$-th element of $a$ in $0$-based indexing, that is, the $1+m$-th element of $a$. In other words, using the ellipsis "$\ldots$", the integer sequence $a$ can be written as

$\displaystyle (a_0, a_1, a_2, a_3, \ldots ) $

.

Whenever we speak of coin tosses, the trials are independent, and in every trial the probability of heads and the probability of tails are both $\frac{1}{2}$.

Coin Toss Loving Bot is, as you know, a bot that loves coin tosses.

For each integer sequence $a$, Coin Toss Loving Bot devised the following single-player game:

1. First, the player chooses any non-negative integer $x$.
2. Next, the player tosses a coin $x$ times; let $m$ be the number of times heads comes up.
3. Finally, the player earns $a_m$ points.

Let us call the game constructed in this way from an integer sequence $a$ "the integer sequence coin toss game associated with $a$".

Now, let us get to the main subject.

One day, Coin Toss Loving Bot wondered how much information about the integer sequence $a$ can be recovered from information about the expected score in the integer sequence coin toss game associated with $a$.

Determine whether there exists an integer sequence $a$ satisfying "for any non-negative integer $X$, the expected score when choosing $X$ as $x$ in the integer sequence coin toss game associated with $a$ is $2^{-X} X^N$", and if one exists, find $1$ possible value of $a_M$ for such an integer sequence $a$.

Input

The input is given from standard input in the following format:

$N$
$M$

Constraints

The input $N,M$ satisfies the following constraints:

• $N$ is a non-negative integer at most $15$
• $M$ is a non-negative integer at most $10^9$

Output

If there exists an integer sequence $a$ such that the expected score when choosing a non-negative integer $X$ as $x$ in the integer sequence coin toss game associated with $a$ is $2^{-X} X^N$, print $1$ possible value of $a_M$ for such an integer sequence $a$ on $1$ line; if none exists, print NaN.

This problem uses a special judge. Even if the correct answer is not limited to $1$ possibility, print only $1$ of them.

Also, due to judging constraints, your output must be at most $100$ characters.

Print a newline at the end.

Sample

1
1

1

2
1

1

3
1

1