20590번 - Biggest Set Ever 다국어

A set of nonnegative integers is fine if and only if all numbers in the set are less than $T$ and their sum is equivalent to $\mathit{rem}$ modulo $n$. Your task is to find the number of different fine sets.

The first line of the input contains space-separated integers $n$ and $\mathit{rem}$ ($0 \le \mathit{rem} < n \le 10^4$). The second line of the input contains a single integer $T$ ($1 \le T \le 10^{100\,000} - 1$).

Print the number of different fine sets. As this number can be really large, you should print it modulo prime number $998\,244\,353$.

In the first sample, we can include or exclude numbers $0$ and $3$ freely, it doesn't change the remainder. From numbers $\{ 1, 2, 4 \}$ there are two fine sets: $\{ 2 \}$ and $\{ 1, 4 \}$. So the answer is $2 \cdot 2 \cdot 2 = 8$.

In the second sample, any subset of $\{ 0, 1, \ldots, 19 \}$ is fine, hence, the answer is $2^{20} = 1\,048\,576$.