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# 1425. Constrained Subsequence Sum

<https://leetcode.com/problems/constrained-subsequence-sum>

## Description

Given an integer array `nums` and an integer `k`, return the maximum sum of a **non-empty** subsequence of that array such that for every two **consecutive** integers in the subsequence, `nums[i]` and `nums[j]`, where `i < j`, the condition `j - i <= k` is satisfied.

A *subsequence* 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.

**Example 1:**

```
**Input:** nums = [10,2,-10,5,20], k = 2
**Output:** 37
**Explanation:** The subsequence is [10, 2, 5, 20].
```

**Example 2:**

```
**Input:** nums = [-1,-2,-3], k = 1
**Output:** -1
**Explanation:** The subsequence must be non-empty, so we choose the largest number.
```

**Example 3:**

```
**Input:** nums = [10,-2,-10,-5,20], k = 2
**Output:** 23
**Explanation:** The subsequence is [10, -2, -5, 20].
```

**Constraints:**

* `1 <= k <= nums.length <= 105`
* `-104 <= nums[i] <= 104`

## ac

```java
```