Problem: Mr. Kitayuta has kindly given you a string s consisting of lowercase English letters. You are asked to insert exactly one lowercase English letter into s to make it a palindrome. A palindrome is a string that reads the same forward and backward. For example, "noon", "testset" and "a" are all palindromes, while "test" and "kitayuta" are not.

You can choose any lowercase English letter, and insert it to any position of s, possibly to the beginning or the end of s. You have to insert a letter even if the given string is already a palindrome.

If it is possible to insert one lowercase English letter into s so that the resulting string will be a palindrome, print the string after the insertion. Otherwise, print "NA" (without quotes, case-sensitive). In case there is more than one palindrome that can be obtained, you are allowed to print any of them.

Input

The only line of the input contains a string s (1 ≤ |s| ≤ 10). Each character in s is a lowercase English letter.

Output

If it is possible to turn s into a palindrome by inserting one lowercase English letter, print the resulting string in a single line. Otherwise, print "NA" (without quotes, case-sensitive). In case there is more than one solution, any of them will be accepted. 

Examples

Input

revive


Output

reviver


Input

ee


Output

eye

Input

kitayuta


Output

NA

Note

For the first sample, insert 'r' to the end of "revive" to obtain a palindrome "reviver".

For the second sample, there is more than one solution. For example, "eve" will also be accepted.

For the third sample, it is not possible to turn "kitayuta" into a palindrome by just inserting one letter.

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;
import java.text.*;
import java.math.*;
import java.util.regex.*;

public class Solution{
	public int solve(String input, int start, int end, int record){
		if(start >= end)
			return record; 
		if(input.charAt(start) == input.charAt(end))
			return solve(input, start + 1, end - 1, record);
		else if(record < 0){
			int tempResult = solve(input, start + 1, end, start);
			if(tempResult < 0)
				tempResult = solve(input, start, end - 1, end);
			return tempResult;
		} else
			return -1;
	}
	public boolean isPalindrome(String input){
		int start = 0, end = input.length() - 1;
		while(start < end){
			if(input.charAt(start) != input.charAt(end))
				return false;
			start ++;
			end --;
		}
		return true;
	}

	public String getResult(String input){
		char[] result = new char[input.length() + 1];
		if(input.length() % 2 == 1){
			for(int i = 0;i < result.length / 2; i++){
				result[i] = input.charAt(i);
				result[result.length - 1 - i] = input.charAt(i);
			}
		}
		else{
			for(int i = 0;i < input.length() / 2; i++){
				result[i] = input.charAt(i);
				result[result.length - 1 - i] = input.charAt(i);
			}
			result[result.length / 2] = 'a';
		}
		return new String(result);
	}

	public String getResult(String input, int record){
		char[] result = new char[input.length() + 1];
		int oldStart = 0, oldEnd = input.length() - 1, newStart = 0, newEnd = result.length - 1;
		while(newStart <= newEnd){
			if(oldStart == record){
				result[newStart++] = input.charAt(oldStart);
				result[newEnd--] = input.charAt(oldStart);
				oldStart ++;
			} else if(oldEnd == record){
				result[newStart++] = input.charAt(oldEnd);
				result[newEnd--] = input.charAt(oldEnd);
				oldEnd --;
			} else{
				result[newStart++] = input.charAt(oldStart++);
				result[newEnd--] = input.charAt(oldEnd --);
			}
		}
		return new String(result);
	}
	public static void main(String[] args){
		Scanner scan = new Scanner(System.in);
		String input = scan.next();
		Solution solution = new Solution();
		if(solution.isPalindrome(input))
			System.out.println(solution.getResult(input));
		else{
			int result = solution.solve(input, 0 , input.length() - 1, -1);
			if(result < 0)
				System.out.println("NA");
			else
				System.out.println(solution.getResult(input, result));
		}
		
	}
}