AT_arc204_a [ARC204A] Use Udon Coupon

You are given positive integers $ N, L, R $ and length- $ N $ positive integer sequences $ A = (A_{1}, A_{2}, \dots, A_{N}), B = (B_{1}, B_{2}, \dots, B_{N}) $ . Using a sequence $ Q $ initialized as empty, a variable $ C $ initialized to $ 0 $ , and a variable $ i $ initialized to $ 1 $ , perform the following operation $ 2N $ times. - Choose one of the following actions $ 1, 2 $ and perform it. - Action $ 1 $ : Insert $ i $ at the end of $ Q $ , replace $ C $ with $ \max(0, C - A_{i}) $ . Then, increase $ i $ by $ 1 $ . This action can only be performed when $ i $ before the operation is at most $ N $ . - Action $ 2 $ : Let $ x $ be the first number in $ Q $ , and add $ B_{x} $ to $ C $ . Then, remove the first element of $ Q $ . This action can only be performed when $ Q $ before the operation is not empty. Find the number, modulo $ 998244353 $ , of ways to perform $ 2N $ operations such that the final value of $ C $ is between $ L $ and $ R $ , inclusive.

The input is given from Standard Input in the following format: > $ N $ $ L $ $ R $ $ A_{1} $ $ A_{2} $ $ \dots $ $ A_{N} $ $ B_{1} $ $ B_{2} $ $ \dots $ $ B_{N} $

Output the answer.

### Sample Explanation 1 For example, you can perform four operations as follows. - Perform action $ 1 $ . Then, $ Q = (1), C = 0, i = 2 $ . - Perform action $ 2 $ . Then, $ Q = (), C = 924, i = 2 $ . - Perform action $ 1 $ . Then, $ Q = (2), C = 757, i = 3 $ . - Perform action $ 2 $ . Then, $ Q = (), C = 935, i = 3 $ . Performing operations as above makes the final value of $ C $ between $ 100 $ and $ 1000 $ (inclusive). This is the only such way to perform operations, so output $ 1 $ . ### Constraints - $ 1\leq N\leq 5000 $ - $ 1\leq L \leq R \leq \sum B $ - $ 1\leq A_{i}\leq 5000 $ - $ 1\leq B_{i}\leq 5000 $ - All input values are integers.