Sum over DP Table Recurrence

Given two integers N and K, you are required to compute

[ S = \sum_{i=1}^{K} f[N][i] \pmod{998244353}, ]

where the two-dimensional array (f[i][j]) is defined by the recurrence

[ f[i][j] = f[i-1][j] + f[i][j-1] + f[i-1][j-1] \quad \text{for } i > 1 \text{ and } j \leq i, ]

with the base conditions

[ f[1][1] = 1, \quad f[i][0] = 0, \quad f[i][j] = 0 \text{ for } j > i. ]

Note that when (K > N), since (f[N][j] = 0) for (j > N), only the values with (1 \leq j \leq N) will contribute to the sum.

Your task is to compute and output S modulo (998244353).

inputFormat

The input consists of a single line containing two space-separated integers, N and K.

outputFormat

Output a single integer representing the value of (S = \sum_{i=1}^{K} f[N][i]) modulo (998244353).

sample

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1