Score : 700 points
Takahashi has a tower which is divided into N layers. Initially, all the layers are uncolored. Takahashi is going to paint some of the layers in red, green or blue to make a beautiful tower. He defines the beauty of the tower as follows:
Here, A and B are positive integer constants given beforehand. Also note that a layer may not be painted in two or more colors.
Takahashi is planning to paint the tower so that the beauty of the tower becomes exactly K. How many such ways are there to paint the tower? Find the count modulo 998244353. Two ways to paint the tower are considered different when there exists a layer that is painted in different colors, or a layer that is painted in some color in one of the ways and not in the other.
Input is given from Standard Input in the following format:
N A B K
Print the number of the ways to paint tiles, modulo 998244353.
4 1 2 5
40
In this case, a red layer worth 1 points, a green layer worth 3 points and the blue layer worth 2 points. The beauty of the tower is 5 when we have one of the following sets of painted layers:
The total number of the ways to produce them is 40.
2 5 6 0
1
The beauty of the tower is 0 only when all the layers are uncolored. Thus, the answer is 1.
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