There is a test that has n types of questions. You are given an integer target and a 0-indexed 2D integer array types where types[i] = [counti, marksi] indicates that there are counti questions of the ith type, and each one of them is worth marksi points.
Return the number of ways you can earn exactly target points in the exam. Since the answer may be too large, return it modulo 109 + 7.
Note that questions of the same type are indistinguishable.
\n\n3 questions of the same type, then solving the 1st and 2nd questions is the same as solving the 1st and 3rd questions, or the 2nd and 3rd questions.\n
Example 1:
\n\n\nInput: target = 6, types = [[6,1],[3,2],[2,3]]\nOutput: 7\nExplanation: You can earn 6 points in one of the seven ways:\n- Solve 6 questions of the 0th type: 1 + 1 + 1 + 1 + 1 + 1 = 6\n- Solve 4 questions of the 0th type and 1 question of the 1st type: 1 + 1 + 1 + 1 + 2 = 6\n- Solve 2 questions of the 0th type and 2 questions of the 1st type: 1 + 1 + 2 + 2 = 6\n- Solve 3 questions of the 0th type and 1 question of the 2nd type: 1 + 1 + 1 + 3 = 6\n- Solve 1 question of the 0th type, 1 question of the 1st type and 1 question of the 2nd type: 1 + 2 + 3 = 6\n- Solve 3 questions of the 1st type: 2 + 2 + 2 = 6\n- Solve 2 questions of the 2nd type: 3 + 3 = 6\n\n\n
Example 2:
\n\n\nInput: target = 5, types = [[50,1],[50,2],[50,5]]\nOutput: 4\nExplanation: You can earn 5 points in one of the four ways:\n- Solve 5 questions of the 0th type: 1 + 1 + 1 + 1 + 1 = 5\n- Solve 3 questions of the 0th type and 1 question of the 1st type: 1 + 1 + 1 + 2 = 5\n- Solve 1 questions of the 0th type and 2 questions of the 1st type: 1 + 2 + 2 = 5\n- Solve 1 question of the 2nd type: 5\n\n\n
Example 3:
\n\n\nInput: target = 18, types = [[6,1],[3,2],[2,3]]\nOutput: 1\nExplanation: You can only earn 18 points by answering all questions.\n\n\n
\n
Constraints:
\n\n1 <= target <= 1000n == types.length1 <= n <= 50types[i].length == 21 <= counti, marksi <= 50考试中有 n 种类型的题目。给你一个整数 target 和一个下标从 0 开始的二维整数数组 types ，其中 types[i] = [counti, marksi] 表示第 i 种类型的题目有 counti 道，每道题目对应 marksi 分。
返回你在考试中恰好得到 target 分的方法数。由于答案可能很大，结果需要对 109 +7 取余。
注意，同类型题目无法区分。
\n\n3 道同类型题目，那么解答第 1 和第 2 道题目与解答第 1 和第 3 道题目或者第 2 和第 3 道题目是相同的。\n\n
示例 1：
\n\n输入：target = 6, types = [[6,1],[3,2],[2,3]]\n输出：7\n解释：要获得 6 分，你可以选择以下七种方法之一：\n- 解决 6 道第 0 种类型的题目：1 + 1 + 1 + 1 + 1 + 1 = 6\n- 解决 4 道第 0 种类型的题目和 1 道第 1 种类型的题目：1 + 1 + 1 + 1 + 2 = 6\n- 解决 2 道第 0 种类型的题目和 2 道第 1 种类型的题目：1 + 1 + 2 + 2 = 6\n- 解决 3 道第 0 种类型的题目和 1 道第 2 种类型的题目：1 + 1 + 1 + 3 = 6\n- 解决 1 道第 0 种类型的题目、1 道第 1 种类型的题目和 1 道第 2 种类型的题目：1 + 2 + 3 = 6\n- 解决 3 道第 1 种类型的题目：2 + 2 + 2 = 6\n- 解决 2 道第 2 种类型的题目：3 + 3 = 6\n\n\n
示例 2：
\n\n输入：target = 5, types = [[50,1],[50,2],[50,5]]\n输出：4\n解释：要获得 5 分，你可以选择以下四种方法之一：\n- 解决 5 道第 0 种类型的题目：1 + 1 + 1 + 1 + 1 = 5\n- 解决 3 道第 0 种类型的题目和 1 道第 1 种类型的题目：1 + 1 + 1 + 2 = 5\n- 解决 1 道第 0 种类型的题目和 2 道第 1 种类型的题目：1 + 2 + 2 = 5\n- 解决 1 道第 2 种类型的题目：5\n\n\n
示例 3：
\n\n输入：target = 18, types = [[6,1],[3,2],[2,3]]\n输出：1\n解释：只有回答所有题目才能获得 18 分。\n\n\n
\n\n
提示：
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