<p>Given an integer array <code>nums</code> and an integer <code>k</code>, return the maximum sum of a <strong>non-empty</strong> subsequence of that array such that for every two <strong>consecutive</strong> integers in the subsequence, <code>nums[i]</code> and <code>nums[j]</code>, where <code>i &lt; j</code>, the condition <code>j - i &lt;= k</code> is satisfied.</p>

<p>A <em>subsequence</em> of an array is obtained by deleting some number of elements (can be zero) from the array, leaving the remaining elements in their original order.</p>

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

<pre>
<strong>Input:</strong> nums = [10,2,-10,5,20], k = 2
<strong>Output:</strong> 37
<b>Explanation:</b> The subsequence is [10, 2, 5, 20].
</pre>

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

<pre>
<strong>Input:</strong> nums = [-1,-2,-3], k = 1
<strong>Output:</strong> -1
<b>Explanation:</b> The subsequence must be non-empty, so we choose the largest number.
</pre>

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

<pre>
<strong>Input:</strong> nums = [10,-2,-10,-5,20], k = 2
<strong>Output:</strong> 23
<b>Explanation:</b> The subsequence is [10, -2, -5, 20].
</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>-10<sup>4</sup> &lt;= nums[i] &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
  int solve1(vector<int>& nums, int k) {
    int n = nums.size();

    int ans = -1e9;
    deque<int> w;
    map<int, int> count;
    for (int i = 0; i < n; ++i) {
      if (w.size() == k + 1) {
        count[w.front()] -= 1;
        if (count[w.front()] == 0) {
          count.erase(w.front());
        }

        w.pop_front();
      }

      int current_max = nums[i];
      if (!count.empty()) {
        int prev_max = count.rbegin()->first;
        if (prev_max > 0) {
          current_max += prev_max;
        }
      }

      w.emplace_back(current_max);
      count[w.back()] += 1;

      ans = max(ans, current_max);
    }

    return ans;
  }

  int constrainedSubsetSum(vector<int>& nums, int k) {
    return solve1(nums, k);
  }
};
163612