Growing Sequences

In scientific research, exponentially growing sequences appear quite often. Some researches are especially interested in integer arrays of length $n$ where each element is at least twice as large as the previous one: formally, $2 \cdot a\_{i} \le a\_{i+1}$ for $1 \leq i \leq n - 1$. They want to calculate the number of different bounded arrays satisfying this condition.

Help them! Count the number of such arrays consisting of integers from $1$ to $c$. Since this number can be very large, you should output it modulo $998\\,244\\,353$.

The only line contains two integers $n$ and $c$ ($1 \le n \le 60$; $1 \le c \le 10^{18}$): the length of the arrays and the maximum value of their elements.

Output the number of different arrays modulo $998\\,244\\,353$.

In the first example, there are $5$ different arrays: $\[1]$, $\[2]$, $\[3]$, $\[4]$, $\[5]$.

In the second example, there are $4$ different arrays: $\[1, 2, 4]$, $\[1, 2, 5]$, $\[1, 2, 6]$, $\[1, 3, 6]$.

In the third example, there are no arrays satisfying the conditions.