E. Expected Snaps
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Thanos has an array whose length is a power of two. Before he sees it, every element is chosen independently and uniformly from the integers $$$1,2,\ldots,K$$$.

An array is sorted if it is nondecreasing. While the current array is not sorted, Thanos performs a snap:

  • with probability $$$1/2$$$, he keeps the left half and discards the right half;
  • with probability $$$1/2$$$, he keeps the right half and discards the left half.

All snap choices are independent of each other and of the initial array. After each snap, he checks the remaining array again. An array of length one is always sorted.

The initial length is $$$N=2^n$$$. Find the expected number of snaps, where the expectation is taken over both the random initial array and all snap choices.

Input

The only line contains two integers $$$n$$$ and $$$K$$$ – the exponent of the initial length and the number of possible values. The value of $$$n$$$ is between 0 and 200000, inclusive, and $$$K$$$ is between 1 and 200000, inclusive.

It is guaranteed that $$$nK$$$ is at most 20000000.

Output

Let the expected number of snaps be the rational number $$$p/q$$$, where $$$p$$$ and $$$q$$$ are coprime. Print the residue modulo 998244353 of the product of $$$p$$$ and $$$q^{-1}$$$, where $$$q^{-1}$$$ is the multiplicative inverse of $$$q$$$ modulo 998244353. It is guaranteed that this inverse exists.

Examples
Input
1 2
Output
748683265
Input
0 1
Output
0
Input
4 5
Output
280149939
Note

For $$$n=1$$$ and $$$K=2$$$, the only unsorted initial array is $$$[2,1]$$$. It requires one snap, so the expectation is $$$1/4$$$.