Find Number 6 Recursively

Background

Congcong is currently learning about recursive algorithms. He encountered an interesting problem that requires determining if a specific number is present in an integer array.

Problem Description

Given an array of integers, compute recursively if the array contains the number $6$. We'll use the convention of considering only the part of the array that begins at the given index. In this way, a recursive call can pass $index+1$ to move down the array. The initial call will pass in $index$ as $0$.

Input Format

Input is given from standard input in the following format.

A single line containing several integers. The last integer represents the starting index $index$, and all preceding integers form the array to be checked.

Output Format

Output is printed to standard output in the following format.

Output true if the array contains $6$; otherwise, output false.

Sample

1 6 4 0

true

1 4 0

false

6 0

true

Sample Explanation

For the first sample 1 6 4 0: The array is [1, 6, 4] and the starting index is $0$. Starting from index $0$, the array element $arr[0]$ is $1$, which is not $6$. A recursive call checks the array part [6, 4] starting from index $1$. $arr[1]$ is $6$, so it returns true.

Constraints

Time limit for each test case is $1$ second, and memory limit is $1024$ KiB.