J. Dimensional Flower
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Alexa, a $$$d$$$-dimensional being, has recently gotten into gardening! To get her garden started, she has planted her first flower at the origin of a $$$d$$$-dimensional grid. Every second, the flower will grow by 1 unit along one of the coordinate axes in a direction away from the origin. Alexa is very excited for how her flower could turn out, so she wants to know: after $$$t$$$ seconds, how many different possible ways could the flower have grown? Since this number could be large, please output it modulo $$$998244353$$$.

Two ways are different if the flower ever grows in a different direction at some time step.

Input

The first line contains two integers $$$d$$$ and $$$t$$$ ($$$1\leq d,t \leq 2\cdot10^5$$$) — the number of dimensions the flower could grow in and the number of seconds the flower grows for.

Output

Output a single integer, the number of different ways the flower could have grown after $$$t$$$ seconds, modulo $$$998244353$$$.

Examples
Input
2 1
Output
4
Input
3 3
Output
126
Input
12345 67890
Output
243978398
Note

In the first sample, the flower grows for one second, and could end up at $$$(0,1), (0,-1), (1,0),$$$ or $$$(-1,0)$$$.

In the second sample, one way the flower could grow is $$$(0,0,0)\rightarrow(0,1,0)\rightarrow(-1,1,0)\rightarrow(-1,2,0)$$$. Note that for the last second, the flower could not grow in a direction like $$$(-1,1,0)\rightarrow(-1,0,0)$$$, since that does not go away from the origin.