Repetitive Palindrome

Time limit1sMemory limit1024 MB

Summary

Given a lowercase string s and integer k, decide if t formed by concatenating k copies of s is a palindrome.

Level: Medium4 of 10
Topics: String, Math, Implementation
Solved: No attempts yet

Problem

You are given a string $s$ of lowercase alphabets and an integer $k$ .

Form a new string $t$ by concatenating $k$ copies of $s$ . Determine whether $t$ is a palindrome, that is, whether it reads the same forward and backward.

Input

The first line contains a string $s$ of lowercase alphabets. ( $1 \le |s| \le 250,000$ )

The second line contains an integer $k$ . ( $1 \le k \le 10^{18}$ )

Output

If $t$ is a palindrome, print YES. Otherwise, print NO.

Examples2

Example 1
Input
```
abc
3
```
Expected output
```
NO
```
Example 2
Input
```
abba
1
```
Expected output
```
YES
```