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.*;
import java.math.BigDecimal;
import java.math.BigInteger;
import java.util.*;

public class Main {
    public static void main (String[] args) {
        FastReader in = new FastReader(System.in);
        FastWriter out = new FastWriter(System.out);

        char[] s = in.next().toCharArray();
        int i = s.length - 1;
        s = Arrays.copyOf(s, s.length + 1);
        s[s.length - 1] = s[0];

        while (i >= 0) {
            if (score(s)) {
                System.out.println(new String(s));
                return;
            }
            s[i + 1] = s[i];
            s[i] = s[s.length - 1 - i];
            i--;
        }
        if (score(s)) {
            System.out.println(new String(s));
            return;
        }
        System.out.println("NA");
    }

    public static boolean score(char[] b) {
        int i = 0, j = b.length - 1;

        while (i < j) {
            if (b[i] != b[j]) {
                return false;
            }
            i++; j--;
        }
        return true;
    }
}

class FastReader {
    private BufferedReader reader;
    private StringTokenizer tokenizer;

    public FastReader(InputStream stream) {
        this.reader = new BufferedReader(new InputStreamReader(stream));
        this.tokenizer = new StringTokenizer("");
    }

    public boolean hasNext() {
        return ensureTokens();
    }

    public String next() {
        return  ensureTokens() ? tokenizer.nextToken() : null;
    }

    private boolean ensureTokens() {
        while(!tokenizer.hasMoreTokens()){
            try{
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (Exception e){
                return false;
            }
        }
        return true;
    }

    public String nextLine() {
        try {
            return reader.readLine();
        } catch (Exception e) {
            return null;
        }
    }

    public char[] nextCharArray() {
        return nextLine().toCharArray();
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public int[] nextIntArray(int size) {
        int[] array = new int[size];
        for (int i = 0; i < size; i++) {
            array[i] = nextInt();
        }
        return array;
    }

    public int[] nextIntArrayOnLine() {
        String line = nextLine();
        String[] tokens = line.split(" ");
        int[] array = new int[tokens.length];
        for (int i = 0; i < tokens.length; i++) {
            array[i] = Integer.parseInt(tokens[i]);
        }
        return array;
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public long[] nextLongArray(int size) {
        long[] array = new long[size];
        for (int i = 0; i < size; i++) {
            array[i] = nextLong();
        }
        return array;
    }

    public float nextFloat() {
        return Float.parseFloat(next());
    }

    public float[] nextFloatArray(int size) {
        float[] array = new float[size];
        for (int i = 0; i < size; i++) {
            array[i] = nextFloat();
        }
        return array;
    }

    public double nextDouble() {
        return Double.parseDouble(next());
    }

    public double[] nextDoubleArray(int size) {
        double[] array = new double[size];
        for (int i = 0; i < size; i++) {
            array[i] = nextDouble();
        }
        return array;
    }

    public short nextShort() {
        return Short.parseShort(next());
    }

    public short[] nextShortArray(int size) {
        short[] array = new short[size];
        for (int i = 0; i < size; i++) {
            array[i] = nextShort();
        }
        return array;
    }

    public BigDecimal nextBigDecimal() {
        return new BigDecimal(next());
    }

    public BigInteger nextBigInteger() {
        return new BigInteger(next());
    }
}

class FastWriter {
    private final PrintWriter printWriter;

    public FastWriter(OutputStream stream) {
        printWriter = new PrintWriter(new BufferedWriter(new OutputStreamWriter(stream)));
    }

    public FastWriter(Writer writer) {
        printWriter = new PrintWriter(writer);
    }

    public void close() {
        printWriter.close();
    }

    public void print(boolean element) {
        printWriter.print(element);
    }

    public void print(char[] element) {
        printWriter.print(element);
    }

    public void print(double element) {
        printWriter.print(element);
    }

    public void print(float element) {
        printWriter.print(element);
    }

    public void print(int element) {
        printWriter.print(element);
    }

    public void print(long element) {
        printWriter.print(element);
    }

    public void print(String element) {
        printWriter.print(element);
    }

    public void print(Object... objects) {
        for (int i = 0; i < objects.length; i++) {
            if (i != 0) {
                printWriter.print(' ');
            }
            printWriter.print(objects[i]);
        }
    }

    public void println(boolean element) {
        printWriter.println(element);
    }

    public void println(char[] element) {
        printWriter.println(element);
    }

    public void println(double element) {
        printWriter.println(element);
    }

    public void println(float element) {
        printWriter.println(element);
    }

    public void println(int element) {
        printWriter.println(element);
    }

    public void println(long element) {
        printWriter.println(element);
    }

    public void println(String element) {
        printWriter.println(element);
    }

    public void println() {
        printWriter.println();
    }

    public void println(Object... objects) {
        print(objects);
        printWriter.println();
    }

    public void printf(String format, Object... args) {
        printWriter.printf(format, args);
    }
}