<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 SegmentTree
{
    public:
    vector<int> tree;
    int n;
    SegmentTree(int n)
    {
        int x=ceil(log2(n));
        int max_size=2*(int)pow(2,x)-1;
        this->n=max_size;
        this->tree.resize(max_size);
    }
    int query(int ql,int qr,int cl,int cr,int node){
        if(cl>=ql && cr<=qr){
            return tree[node];
        }
        if(cr<ql||cl>qr){
            return 0;
        }
        int mid=(cl+cr)/2;
        int x=query(ql,qr,cl,mid,2*node+1),y=query(ql,qr,mid+1,cr,2*node+2);
        return max(x,y);
    }
    void update(int idx,int val, int cl,int cr,int pos){
        if(pos<cl||pos>cr)return;
        
        if(cl==cr){
            tree[idx]=val;
            return;
        }
        int mid=(cl+cr)/2;
        update(2*idx+1,val,cl,mid,pos);
        update(2*idx+2,val,mid+1,cr,pos);
        tree[idx]=max(tree[2*idx+1],tree[2*idx+2]);
    }
};
class Solution {
public:
    int constrainedSubsetSum(vector<int>& nums, int k) {
        SegmentTree t(nums.size());
    
        for(int i=0;i<nums.size();i++){
            int left=max(0,i-k),right=max(0,i-1);
            int x=t.query(left,right,0,nums.size()-1,0);
            t.update(0,nums[i]+x,0,nums.size()-1,i);
        }
        return t.tree[0];
    }
};
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