{ "data": { "question": { "questionId": "3091", "questionFrontendId": "2902", "categoryTitle": "Algorithms", "boundTopicId": 2473947, "title": "Count of Sub-Multisets With Bounded Sum", "titleSlug": "count-of-sub-multisets-with-bounded-sum", "content": "

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

\n\n

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

\n\n

Since the answer may be large, return it modulo 109 + 7.

\n\n

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.

\n\n

Note that:

\n\n\n\n

 

\n

Example 1:

\n\n
\nInput: nums = [1,2,2,3], l = 6, r = 6\nOutput: 1\nExplanation: The only subset of nums that has a sum of 6 is {1, 2, 3}.\n
\n\n

Example 2:

\n\n
\nInput: nums = [2,1,4,2,7], l = 1, r = 5\nOutput: 7\nExplanation: 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}.\n
\n\n

Example 3:

\n\n
\nInput: nums = [1,2,1,3,5,2], l = 3, r = 5\nOutput: 9\nExplanation: 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}.
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "和带限制的子多重集合的数目", "translatedContent": "

给你一个下标从 0 开始的非负整数数组 nums 和两个整数 l 和 r 。

\n\n

请你返回 nums 中子多重集合的和在闭区间 [l, r] 之间的 子多重集合的数目 。

\n\n

由于答案可能很大，请你将答案对 109 + 7 取余后返回。

\n\n

子多重集合 指的是从数组中选出一些元素构成的 无序 集合，每个元素 x 出现的次数可以是 0, 1, ..., occ[x] 次，其中 occ[x] 是元素 x 在数组中的出现次数。

\n\n

注意：

\n\n\n\n

 

\n\n

示例 1：

\n\n
\n输入：nums = [1,2,2,3], l = 6, r = 6\n输出：1\n解释：唯一和为 6 的子集合是 {1, 2, 3} 。\n
\n\n

示例 2：

\n\n
\n输入：nums = [2,1,4,2,7], l = 1, r = 5\n输出：7\n解释：和在闭区间 [1, 5] 之间的子多重集合为 {1} ，{2} ，{4} ，{2, 2} ，{1, 2} ，{1, 4} 和 {1, 2, 2} 。\n
\n\n

示例 3：

\n\n
\n输入：nums = [1,2,1,3,5,2], l = 3, r = 5\n输出：9\n解释：和在闭区间 [3, 5] 之间的子多重集合为 {3} ，{5} ，{1, 2} ，{1, 3} ，{2, 2} ，{2, 3} ，{1, 1, 2} ，{1, 1, 3} 和 {1, 2, 2} 。
\n\n

 

\n\n

提示：

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