<p>Given an array of <strong>distinct</strong> integers <code>nums</code> and a target integer <code>target</code>, return <em>the number of possible combinations that add up to</em>&nbsp;<code>target</code>.</p>

<p>The test cases are generated so that the answer can fit in a <strong>32-bit</strong> integer.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,2,3], target = 4
<strong>Output:</strong> 7
<strong>Explanation:</strong>
The possible combination ways are:
(1, 1, 1, 1)
(1, 1, 2)
(1, 2, 1)
(1, 3)
(2, 1, 1)
(2, 2)
(3, 1)
Note that different sequences are counted as different combinations.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [9], target = 3
<strong>Output:</strong> 0
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 200</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
	<li>All the elements of <code>nums</code> are <strong>unique</strong>.</li>
	<li><code>1 &lt;= target &lt;= 1000</code></li>
</ul>

<p>&nbsp;</p>
<p><strong>Follow up:</strong> What if negative numbers are allowed in the given array? How does it change the problem? What limitation we need to add to the question to allow negative numbers?</p>

class Solution:
    def combinationSum4(self, nums: List[int], target: int) -> int:
        cache = [0] * (target + 1)
        cache[0] = 1
        for tgt in range(len(cache)):
            for num in nums:
                if tgt >= num and cache[tgt - num]:
                    cache[tgt] += cache[tgt - num]
        return cache[-1]

16100