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 $998\\, 244\\, 353$.