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] = [count_i, marks_i] indicates that there are count_i questions of the i^th type, and each one of them is worth marks_i 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.

For example, if there are 3 questions of the same type, then solving the 1^st and 2^nd questions is the same as solving the 1^st and 3^rd questions, or the 2^nd and 3^rd questions.

Example 1:

Input: target = 6, types = [[6,1],[3,2],[2,3]]
Output: 7
Explanation: You can earn 6 points in one of the seven ways:
- Solve 6 questions of the 0^th type: 1 + 1 + 1 + 1 + 1 + 1 = 6
- Solve 4 questions of the 0^th type and 1 question of the 1^st type: 1 + 1 + 1 + 1 + 2 = 6
- Solve 2 questions of the 0^th type and 2 questions of the 1^st type: 1 + 1 + 2 + 2 = 6
- Solve 3 questions of the 0^th type and 1 question of the 2^nd type: 1 + 1 + 1 + 3 = 6
- Solve 1 question of the 0^th type, 1 question of the 1^st type and 1 question of the 2^nd type: 1 + 2 + 3 = 6
- Solve 3 questions of the 1^st type: 2 + 2 + 2 = 6
- Solve 2 questions of the 2^nd type: 3 + 3 = 6

Example 2:

Input: target = 5, types = [[50,1],[50,2],[50,5]]
Output: 4
Explanation: You can earn 5 points in one of the four ways:
- Solve 5 questions of the 0^th type: 1 + 1 + 1 + 1 + 1 = 5
- Solve 3 questions of the 0^th type and 1 question of the 1^st type: 1 + 1 + 1 + 2 = 5
- Solve 1 questions of the 0^th type and 2 questions of the 1^st type: 1 + 2 + 2 = 5
- Solve 1 question of the 2^nd type: 5

Example 3:

Input: target = 18, types = [[6,1],[3,2],[2,3]]
Output: 1
Explanation: You can only earn 18 points by answering all questions.

Constraints:

1 <= target <= 1000
n == types.length
1 <= n <= 50
types[i].length == 2
1 <= count_i, marks_i <= 50

Number of Ways to Earn Points

Problem Description

Problem Description

Answer Panel