Problem: Mr. Kitayuta has kindly given you a string s consisting of lowercase English letters. You are asked to insert exactly n lowercase English letters 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 n lowercase English letters, and insert each of them to any position of s, possibly to the beginning or the end of s. You have to insert exactly n letters even if it is possible to turn s into a palindrome by inserting less than n letters.

Find the number of the palindromes that can be obtained in this way, modulo 10007.

Input

The first line contains a string s (1 ≤ |s| ≤ 200). Each character in s is a lowercase English letter.

The second line contains an integer n (1 ≤ n ≤ 109).

Output

Print the number of the palindromes that can be obtained, modulo 10007.

Examples

Input

revive
1


Output

1


Input

add
2


Output

28

Note

For the first sample, you can obtain the palindrome "reviver" by inserting 'r' to the end of "revive".

For the second sample, the following 28 palindromes can be obtained: "adada", "adbda", ..., "adzda", "dadad" and "ddadd".

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Iterator;

public class C505A {
    private static String NA = "NA";

    public static class Palyndrom implements Iterable {
        private char[] string;

        private char markedChar;
        private int markedPosition;

        public static String create(char[] string, char ch, int pos) {
            int left = 0;
            int right = string.length - 1;
            char[] newString = new char[string.length + 2];
            int newLeft = 0;
            int newRight = newString.length - 1;

            while (left <= right) {
                if (newLeft == pos || newRight == pos + 1) {
                    newString[newLeft++] = ch;
                    newString[newRight--] = ch;
                }

                newString[newLeft++] = string[left++];
                newString[newRight--] = string[right--];
            }
            return String.valueOf(newString);
        }

        public static String addChar(char[] string) {
            int left = 0;
            int right = string.length - 1;
            char[] newString = new char[string.length + 1];
            int newLeft = 0;
            int newRight = newString.length - 1;

            while (left <= right) {
                if (right - left == 1) {
                    newString[newLeft++] = string[left++];
                    newString[newRight--] = string[right--];
                    newString[newLeft] = 'y';
                } else if (left == right) {
                    newString[newLeft++] = string[left];
                    newString[newLeft] = string[left++];
                } else {
                    newString[newLeft++] = string[left++];
                    newString[newRight--] = string[right--];
                }
            }

            return String.valueOf(newString);
        }

        public Palyndrom(char[] string) {
            this.string = string;
        }

        public Palyndrom(String string) {
            this.string = string.toCharArray();
        }

        public boolean hasIt() {
            int left = 0;
            int right = string.length - 1;

            while (left <= right) {
                if (string[left++] != string[right--]) {
                    return false;
                }
            }
            return string.length > 0;
        }

        private class PalyndromIterator implements Iterator {
            private int position = 0;

            public PalyndromIterator() {
            }

            @Override
            public boolean hasNext() {
                if (string.length > 1) {
                    return position < string.length;
                }
                return false;
            }

            @Override
            public Object next() {
                char[] p = new char[string.length - 1];
                int i = 0;

                for (int index = 0; index < string.length; index++) {
                    if (position == index) {
                        markedChar = string[position];
                        markedPosition = position;

                        continue;
                    }
                    p[i++] = string[index];
                }
                position++;

                return new Palyndrom(p);
            }

            @Override
            public void remove() {

            }
        }

        @Override
        public Iterator iterator() {
            return new PalyndromIterator();
        }

        public String getString() {
            return String.valueOf(string);
        }

        public char getMarkedChar() {
            return markedChar;
        }

        public int getMarkedPosition() {
            return markedPosition;
        }
    }

    public static void main(String[] args) throws IOException {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        Palyndrom palyndrom = new Palyndrom(reader.readLine());
        reader.close();

        if (palyndrom.hasIt()) {
            System.out.println(Palyndrom.addChar(palyndrom.getString().toCharArray()));
        } else {
            Palyndrom miniPalyndrom = null;
            Iterator<Palyndrom> iter = palyndrom.iterator();
            while (iter.hasNext()) {
                Palyndrom p = iter.next();

                if (p.hasIt()) {
                    miniPalyndrom = p;
                    break;
                }
            }

            if (miniPalyndrom == null) {
                System.out.println(NA);
            } else {
                System.out.println(Palyndrom.create(miniPalyndrom.getString().toCharArray(), palyndrom.getMarkedChar(), palyndrom.getMarkedPosition()));
            }
        }
    }
}