<p>You are given a <strong>0-indexed</strong> array of integers <code>nums</code>, and an integer <code>target</code>.</p>

<p>Return <em>the <strong>length of the longest subsequence</strong> of</em> <code>nums</code> <em>that sums up to</em> <code>target</code>. <em>If no such subsequence exists, return</em> <code>-1</code>.</p>

<p>A <strong>subsequence</strong> is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.</p>

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

<pre>
<strong>Input:</strong> nums = [1,2,3,4,5], target = 9
<strong>Output:</strong> 3
<strong>Explanation:</strong> There are 3 subsequences with a sum equal to 9: [4,5], [1,3,5], and [2,3,4]. The longest subsequences are [1,3,5], and [2,3,4]. Hence, the answer is 3.
</pre>

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

<pre>
<strong>Input:</strong> nums = [4,1,3,2,1,5], target = 7
<strong>Output:</strong> 4
<strong>Explanation:</strong> There are 5 subsequences with a sum equal to 7: [4,3], [4,1,2], [4,2,1], [1,1,5], and [1,3,2,1]. The longest subsequence is [1,3,2,1]. Hence, the answer is 4.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,5,4,5], target = 3
<strong>Output:</strong> -1
<strong>Explanation:</strong> It can be shown that nums has no subsequence that sums up to 3.
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 1000</code></li>
	<li><code>1 &lt;= nums[i] &lt;= 1000</code></li>
	<li><code>1 &lt;= target &lt;= 1000</code></li>
</ul>

class Solution:
    def lengthOfLongestSubsequence(self, nums: List[int], target: int) -> int:

        # for every value, can add or not
        # memo = dict()
        # def length(i, target):
        #     if (i, target) in memo:
        #         return memo[(i, target)]
        #     if target == 0:
        #         return 0
        #     if i == len(nums):
        #         return -float('inf')
        #     if target < 0:
        #         return -float('inf')

        #     ans = max(1 + length(i+1, target - nums[i]), length(i+1, target))
        #     memo[(i, target)] = ans
        #     return ans

        # ans = length(0, target)
        # return ans if ans != -float('inf') else -1

        dp = [[-float('inf')] * (target+1) for _ in range(len(nums)+1)]
        for i in range(len(nums)+1):
            dp[i][0] = 0 # if amount 0, then 0 length
        for j in range(1, target+1):
            for i in range(len(nums)-1,-1,-1):
                dp[i][j] = max(1 + (dp[i+1][j-nums[i]] if j-nums[i] >= 0 else -float('inf')), dp[i+1][j])
        
        return dp[0][target] if dp[0][target] != -float('inf') else -1

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