Statement

Let the coefficients of a linear equation with $n$ variables all be 1, and its sum be $m$. Find the number of non-negative integer solutions to this equation modulo 998244353.

In other words, we are seeking the number of non-negative integer solutions to the equation

Since the answer may be very large, please provide the value of the result modulo 998244353.

Input

A line containing two integers $n$ and $m$ separated by a space, where $1\leqslant n,m\leqslant 1\times 10^3$.

Output

Output an integer representing the value of the number of non-negative integer solutions to the equation modulo 998244353.

Samples

2 3

4

3 4

15

Notes

The possible outcomes for the first set of samples, $x_1+x_2=3$, are:

1. $x_1=0,x_2=3$,
2. $x_1=1,x_2=2$,
3. $x_1=2,x_2=1$,
4. $x_1=3,x_2=0$.

There are 4 sets of solutions.