2902 - Count of Sub-Multisets With Bounded Sum\.

Hard

You are given a 0-indexed array nums of non-negative integers, and two integers l and r.

Return the count of sub-multisets within nums where the sum of elements in each subset falls within the inclusive range of [l, r].

Since the answer may be large, return it modulo <code>10⁹ + 7</code>.

A sub-multiset is an unordered collection of elements of the array in which a given value x can occur 0, 1, ..., occ[x] times, where occ[x] is the number of occurrences of x in the array.

Note that:

• Two sub-multisets are the same if sorting both sub-multisets results in identical multisets.

• The sum of an empty multiset is 0.

Example 1:

Input: nums = 1,2,2,3, l = 6, r = 6

Output: 1

Explanation: The only subset of nums that has a sum of 6 is {1, 2, 3}.

Example 2:

Input: nums = 2,1,4,2,7, l = 1, r = 5

Output: 7

Explanation: The subsets of nums that have a sum within the range 1, 5 are {1}, {2}, {4}, {2, 2}, {1, 2}, {1, 4}, and {1, 2, 2}.

Example 3:

Input: nums = 1,2,1,3,5,2, l = 3, r = 5

Output: 9

Explanation: The subsets of nums that have a sum within the range 3, 5 are {3}, {5}, {1, 2}, {1, 3}, {2, 2}, {2, 3}, {1, 1, 2}, {1, 1, 3}, and {1, 2, 2}.

Constraints:

• <code>1 <= nums.length <= 2 * 10⁴</code>

• <code>0 <= numsi<= 2 * 10⁴</code>

• Sum of nums does not exceed <code>2 * 10⁴</code>.

• <code>0 <= l <= r <= 2 * 10⁴</code>