P8735 [Lanqiao Cup 2020 National A] Blue Jumper

Xiaolan built a robot named Blue Jumper, because when this robot walks, it mostly moves by jumping. Blue Jumper can move forward by jumping, and it can also turn around. The length of each jump must be an integer, and each jump can be at most $k$. Because Blue Jumper is not very well balanced, if it makes two consecutive jumps, and both jump lengths are at least $p$, then Blue Jumper will fall down, which Xiaolan does not want to see. Xiaolan received a special task: to show Blue Jumper on a stage of length $L$. Xiaolan needs to control Blue Jumper to go from the left side of the stage to the right side, then turn around, then go from right to left, then turn around, then go from left to right, then turn around, then go from right to left, then turn around, and so on repeatedly. To keep the audience from getting bored, Xiaolan decides to make Blue Jumper use a different way to walk each time. Xiaolan records the jump length of each step, in order, as a sequence. Clearly, every number in this sequence is at most $k$, and the sum is $L$. One trip from one side of the stage to the other produces one such sequence. If two sequences have different lengths, or if there exists some position where the numbers differ, then they are considered different plans. Given that Blue Jumper must not fall down, how many different plans are there for it to go from one side of the stage to the other?

One line contains three integers $k, p, L$.

Output one integer representing the answer. The answer may be very large; output the remainder of the answer divided by $20201114$.

**[Sample Explanation]** Blue Jumper has the following 9 jumping methods: 1. $1+1+1+1+1$ 2. $1+1+1+2$ 3. $1+1+2+1$ 4. $1+2+1+1$ 5. $2+1+1+1$ 6. $2+1+2$ 7. $1+1+3$ 8. $1+3+1$ 9. $3+1+1$ **[Constraints and Notes for Test Cases]** For $30\%$ of the test cases, $1 \leq p \leq k \leq 50, 1 \leq L \leq 1000$. For $60\%$ of the test cases, $1 \leq p \leq k \leq 50, 1 \leq L \leq 10^{9}$. For $80\%$ of the test cases, $1 \leq p \leq k \leq 200, 1 \leq L \leq 10^{18}$. For all test cases, $1 \leq p \leq k \leq 1000, 1 \leq L \leq 10^{18}$. Lanqiao Cup 2020 National Contest Group A, Problem J. Translated by ChatGPT 5