Just in case somebody missed it: this winter is totally cold in Nvodsk! It is so cold that one gets funny thoughts. For example, let's say there are strings with the length exactly n, based on the alphabet of size m. Any its substring with length equal to k is a palindrome. How many such strings exist? Your task is to find their quantity modulo 1000000007 (109 + 7). Be careful and don't miss a string or two!

Let us remind you that a string is a palindrome if it can be read the same way in either direction, from the left to the right and from the right to the left.

Input

The first and only line contains three integers: n, m and k (1 ≤ n, m, k ≤ 2000).

Output

Print a single integer — the number of strings of the described type modulo 1000000007 (109 + 7).

Examples

Input

1 1 1


Output

1


Input

5 2 4


Output

2

Note

In the first sample only one string is valid: "a" (let's denote the only letter of our alphabet as "a").

In the second sample (if we denote the alphabet letters as "a" and "b") the following strings are valid: "aaaaa" and "bbbbb".
import java.io.IOException;
import java.io.InputStream;
import java.math.BigInteger;
import java.util.InputMismatchException;

public class R107_D2_D {
    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        int n = in.readInt();
        int m = in.readInt();
        int k = in.readInt();
        BigInteger res = BigInteger.valueOf(m);
        BigInteger mod = BigInteger.valueOf(1000000007);
        if (k == n) {
            int num = (k + 1) / 2;
            res = res.modPow(BigInteger.valueOf(num), mod);
            System.out.println(res);
        } else if (k > n || k==1) {
            res = res.modPow(BigInteger.valueOf(n), mod);
            System.out.println(res);
        } else if (k % 2 == 0) {
            System.out.println(res);
        } else {
            res = res.modPow(BigInteger.valueOf(2), mod);
            System.out.println(res);
        }
    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1000];
        private int curChar, numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        private int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0)
                    return -1;
            }
            return buf[curChar++];
        }

        public int readInt() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long readLong() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public String readString() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuffer res = new StringBuffer();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        private boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        private String readLine0() {
            StringBuffer buf = new StringBuffer();
            int c = read();
            while (c != '\n' && c != -1) {
                buf.appendCodePoint(c);
                c = read();
            }
            return buf.toString();
        }

        public String readLine() {
            String s = readLine0();
            while (s.trim().length() == 0)
                s = readLine0();
            return s;
        }

        public String readLine(boolean ignoreEmptyLines) {
            if (ignoreEmptyLines)
                return readLine();
            else
                return readLine0();
        }

        public char readCharacter() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            return (char) c;
        }

        public double readDouble() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            double res = 0;
            while (!isSpaceChar(c) && c != '.') {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, readInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = read();
            }
            if (c == '.') {
                c = read();
                double m = 1;
                while (!isSpaceChar(c)) {
                    if (c == 'e' || c == 'E')
                        return res * Math.pow(10, readInt());
                    if (c < '0' || c > '9')
                        throw new InputMismatchException();
                    m /= 10;
                    res += (c - '0') * m;
                    c = read();
                }
            }
            return res * sgn;
        }
    }

}
