5337: Product

Bob has three integers n,k,D.
For a non-negative integer sequence a_1...n, we denote the weight of it is:
D! / （∏_i=1ⁿ (a_i+k)!）
Now Bob wants to know the sum of the weight of all of the sequences a_1...n which satisfies the following conditions:

1. ∀i∈[1,n],a_i≥0
2. ∑_i=1ⁿ a_i=D

If the answer is irreducible fraction x/y, you need to output an integer dd in [0,998244352] which satisfies d * y mod 998244353=x mod 998244353.  
It's guaranteed that y mod 998244353≠0.

The first line has three integers n,k,D.
1≤n≤50.
0≤k≤50.
0≤D≤10⁸.

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