Array Multiple Search

Background

This is an exercise problem about recursion and array traversal.

Problem Description

Given an array of integers, compute recursively if the array contains somewhere a value followed in the array by that value times $10$. 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 an integer array (enclosed in square brackets, elements separated by spaces) and an integer $index$.

Output Format

Output to standard output in the following format.

Output true if such a value exists; otherwise, output false.

Sample

[1 2 20] 0

true

[3 30] 0

true

[3] 0

false

Sample Explanation

Sample 1: For array [1, 2, 20] and starting index $0$.

• When $index = 0$, `arr[0] = 1$. There is no $10 \times 1 = 10$ after $1$ in the array.
• When $index = 1$, arr[1] = 2$. There is $10 \times 2 = 20$ after $2$ in the array (i.e., arr[2]). Thus, true` is returned.

Sample 2: For array [3, 30] and starting index $0$.

• When $index = 0$, arr[0] = 3$. There is $10 \times 3 = 30$ after $3$ in the array (i.e., arr[1]). Thus, true` is returned.

Sample 3: For array [3] and starting index $0$.

• When $index = 0$, arr[0] = 3$. There is no $10 \times 3 = 30$ after $3$ in the array. The array ends, thus false` is returned.

Constraints

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