<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>

from collections import defaultdict
class Solution:
    def lengthOfLongestSubsequence(self, nums: List[int], target: int) -> int:
        return find_lenght_of_longest_subsequence(nums, target)

def find_lenght_of_longest_subsequence(nums, target):
    # Use prefix sum
    log = {0: 0} # storing the prefix sum and the indicies leading to the sum

    for num in nums:
        for prefix_sum in sorted(log, reverse=True):
            cur_sum = prefix_sum + num
            if cur_sum <= target:
                log[cur_sum] = max(log.get(cur_sum, 0), log[prefix_sum] + 1)
    

    return log.get(target, -1)



def find_length_of_longest_contiguous_subsequence(nums, target):
    # Use prefix sum
    log = {} # Store prefix sum at certain index
    current_sum = 0
    max_len = 0

    for i_r, num in enumerate(nums):
        current_sum += num

        if target - current_sum in log:
            i_l = log[target - current_sum]
            length = i_r - i_l + 1
            max_len = max(max_len, length)
        else:
            log[current_sum] = i_r


    return max_len
2824