Numbers Combination

You are given two integers, $N$ and $K$. Determine the number of sequences of integers $(A_1, A_2, \dots , A_N )$ that satisfy

• $1 ≤ A_i ≤ i$ for $1 ≤ i ≤ N$, and
• $A_1 + A_2 + \cdots + A_N = K$.

Since the answer can be very large, calculate the answer modulo $998\, 244\, 353$.

Input consists of two integers $N$ $K$ ($1 ≤ N ≤ 100\, 000$; $N ≤ K ≤ 200\, 000$).

Output in a line an integer representing the answer modulo $998\, 244\, 353$.