656. Coin Path

Given an array A (index starts at 1 ) consisting of N integers: A ₁ , A ₂ , ..., A _N  and an integer B . The integer B denotes that from any place (suppose the index is i ) in the array A , you can jump to any one of the place in the array A indexed i+1 , i+2 , …, i+B if this place can be jumped to. Also, if you step on the index i , you have to pay A _i  coins. If A _i  is -1, it means you can’t jump to the place indexed i in the array.

Now, you start from the place indexed 1 in the array A , and your aim is to reach the place indexed N using the minimum coins. You need to return the path of indexes (starting from 1 to N) in the array you should take to get to the place indexed N using minimum coins.

If there are multiple paths with the same cost, return the lexicographically smallest such path.

If it's not possible to reach the place indexed N then you need to return an empty array.

Example 1:

Input:

 [1,2,4,-1,2], 2
Output:

 [1,3,5]

 

Example 2:

Input:

 [1,2,4,-1,2], 1
Output:

 []

 

Note:

1. Path Pa ₁ , Pa ₂ , ..., Pa _n  is lexicographically smaller than Pb ₁ , Pb ₂ , ..., Pb _m , if and only if at the first i where Pa _i  and Pb _i  differ, Pa _i  < Pb _i ; when no such  i  exists, then  n < m .
2. A ₁ >= 0. A ₂ , ..., A _N (if exist) will in the range of [-1, 100].
3. Length of A is in the range of [1, 1000].
4. B is in the range of [1, 100].