### Instruction:
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.

*   For example, if there are `3` 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.

**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 0th type: 1 + 1 + 1 + 1 + 1 + 1 = 6
- Solve 4 questions of the 0th type and 1 question of the 1st type: 1 + 1 + 1 + 1 + 2 = 6
- Solve 2 questions of the 0th type and 2 questions of the 1st type: 1 + 1 + 2 + 2 = 6
- Solve 3 questions of the 0th type and 1 question of the 2nd type: 1 + 1 + 1 + 3 = 6
- Solve 1 question of the 0th type, 1 question of the 1st type and 1 question of the 2nd type: 1 + 2 + 3 = 6
- Solve 3 questions of the 1st type: 2 + 2 + 2 = 6
- Solve 2 questions of the 2nd 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 0th type: 1 + 1 + 1 + 1 + 1 = 5
- Solve 3 questions of the 0th type and 1 question of the 1st type: 1 + 1 + 1 + 2 = 5
- Solve 1 questions of the 0th type and 2 questions of the 1st type: 1 + 2 + 2 = 5
- Solve 1 question of the 2nd 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 <= counti, marksi <= 50`


### Response:


def numberOfWays(target, types):
    MOD = 10**9 + 7
    dp = [0] * (target + 1)
    dp[0] = 1
    for count, marks in types:
        dptmp = [0] * (target + 1)
        for i in range(target + 1):
            for j in range(count + 1):
                if j * marks + i <= target:
                    dptmp[i + j * marks] = (dptmp[i + j * marks] + dp[i]) % MOD
        dp = dptmp
    return dp[target]
