Prefix String Search

Background

Congcong has been studying string properties recently. He finds many interesting patterns hidden within strings.

Problem Description

Given a string $s$ and an integer $N$, consider the prefix string made of the first $N$ characters of $s$. Determine if this prefix string appears somewhere else in the original string $s$ (i.e., not starting at index $0$). Assume that the string $s$ is not empty and that $N$ is in the range $1 \le N \le |s|$.

Input Format

Input is given from standard input in the following format.

The first line contains a string $s$. The second line contains an integer $N$.

Output Format

Output is printed to standard output in the following format.

Output true if the prefix string appears elsewhere; otherwise, output false.

Sample

abXYabc
1

true

abXYabc
2

true

abXYabc
3

false

Sample Explanation

For the first sample, the string is "abXYabc" and $N=1$. The prefix string is "a". It appears again in the original string starting at index $5$, so the output is true. For the second sample, the string is "abXYabc" and $N=2$. The prefix string is "ab". It appears again in the original string starting at index $5$, so the output is true. For the third sample, the string is "abXYabc" and $N=3$. The prefix string is "abX". It does not appear anywhere else in the original string besides starting at index $0$, so the output is false.

Constraints

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