33376번 - Growing Sequences 다국어

문제

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ドル \cdot a_{i} \le a_{i+1}$ for 1ドル \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ドル$ to $c$. Since this number can be very large, you should output it modulo 998ドル,244円,353円$.

입력

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

출력

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

제한

노트

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

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

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