Leetcode 2902. Count of Sub-Multisets With Bounded Sum

Count the number of sub-multisets (you may take each value 0..occurrence times) whose element sum lies in [l, r], returning the result modulo 1e9+7. Algorithmically this is a bounded subset-sum/counting problem (bounded knapsack) with total sum ≤ 2·10^4, making DP or generating-function techniques appropriate.