Group Sum (Must Include 6)

Background

Congcong is playing a number game. He has a list of integers and needs to select some of them such that their sum equals a given target value. However, there's a special rule: if the number $6$ appears in the list, all occurrences of $6$ must be selected.

Problem Description

Given an array of ints, is it possible to choose a group of some of the ints, beginning at the start index, such that the group sums to the given target? However, with the additional constraint that all $6$'s must be chosen. (No loops needed.)

Input Format

Input is given from standard input in the following format.

start nums target

Where start is an integer representing the starting index; nums is an array of integers; target is an integer representing the target sum.

Output Format

Output is printed to standard output in the following format.

true or false

Output true if a valid group of numbers can be chosen, otherwise output false.

Sample

0 [5 6 2] 8

true

0 [5 6 2] 9

false

0 [5 6 2] 7

false

Sample Explanation

For Sample 1: start = 0, nums = [5, 6, 2], target = 8. Since the array contains $6$, $6$ must be chosen. The remaining target is $8 - 6 = 2$. From the remaining numbers $[5, 2]$, choosing $2$ achieves the target sum of $2$. Thus, choosing $6$ and $2$ results in a sum of $8$, so true is output.

Constraints

Time limit: $1$ second, Memory limit: $1024$ KiB for each test case.