# ---
# title: 1425. Constrained Subsequence Sum
# id: problem1425
# author: Tian Jun
# date: 2020-10-31
# difficulty: Hard
# categories: Dynamic Programming
# link: <https://leetcode.com/problems/constrained-subsequence-sum/description/>
# hidden: true
# ---
# 
# 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 <= 10^5`
#   * `-10^4 <= nums[i] <= 10^4`
# 
# 
## @lc code=start
using LeetCode

## add your code here:
## @lc code=end
