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.*;
import java.util.*;
import java.util.zip.ZipEntry;
import java.math.*;

public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		Input in = new Input(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		Task solver = new Task();
		solver.solve(1, in, out);
		out.close();
	}
}

class Task {
	static final long MOD = 1000000007;
	int[] primes;

	public void solve(int testNumber, Input in, PrintWriter out) {
		long n = in.nextLong();
		long m = in.nextLong();
		long k = in.nextLong();
		long ans = 0;
		if (k == 1 || k > n)
			ans = modPow(m, n);
		else if (k == n) {
			ans = modPow(m, (n + 1) >> 1);
		} else {
			if ((k & 1) == 0) {
				ans = m;
			} else {
				ans = modPow(m, 2);
			}
		}
		out.println(ans);
	}

	// didn't test
	static class BIT {
		int[] MAX;
		int[] MIN;
		int[] SUM;
		int n;

		public BIT(int n) {
			MAX = new int[n + 1];
			MIN = new int[n + 1];
			SUM = new int[n + 1];
			this.n = n;
		}

		public void setSum(int pos, int val) {
			for (int i = pos; i < n; i += (i & -i)) {
				SUM[i] += val;
			}
		}

		public int getSum(int to) {
			int sum = 0;
			for (int i = to; i > 0; i -= (i & -i)) {
				sum += SUM[i];
			}
			return sum;
		}

		public int getSum(int from, int to) {
			return getSum(to) - getSum(from);
		}

		public void setMax(int pos, int val) {
			for (int i = pos; i < n; i += (i & -i)) {
				MAX[i] = Math.max(val, MAX[i]);
			}
		}

		public int getMax(int to) {
			int max = 0;
			for (int i = to; i > 0; i -= (i & -i)) {
				max = Math.max(max, MAX[i]);
			}
			return max;
		}

		public void setMin(int pos, int val) {
			for (int i = pos; i < n; i += (i & -i)) {
				MIN[i] = Math.min(val, MIN[i]);
			}
		}

		public int getMin(int to) {
			int min = 0;
			for (int i = to; i > 0; i -= (i & -i)) {
				min = Math.min(min, MIN[i]);
			}
			return min;
		}

	}

	// didn't test
	static class DisjointSet {
		int[] set;

		public DisjointSet(int n) {
			set = new int[n];
			for (int i = 0; i < n; i++) {
				set[i] = i;
			}
		}

		public int findSet(int a) {
			if (set[a] == a)
				return a;
			return findSet(set[a]);
		}

		public void unionSet(int a, int b) {
			set[findSet(a)] = findSet(b);
		}

		public boolean isSameSet(int a, int b) {
			return findSet(a) == findSet(b);
		}
	}

	static class SegmentTree {
		int[] MAX;
		int[] MIN;
		int[] SUM;
		int[] data;
		int n;

		public SegmentTree(int[] data) {
			this.n = data.length;
			this.data = data;
			MAX = new int[4 * n + 10];
			MIN = new int[4 * n + 10];
			SUM = new int[4 * n + 10];
			buildTree(1, 0, n - 1);
		}

		public int left(int root) {
			return root << 1;
		}

		public int right(int root) {
			return (root << 1) + 1;
		}

		private void buildTree(int root, int rl, int rr) {
			if (rr == rl) {
				MAX[root] = MIN[root] = SUM[root] = data[rr];
			} else {
				int rm = (rl + rr) >> 1;
				buildTree(left(root), rl, rm);
				buildTree(right(root), rm + 1, rr);
				MAX[root] = Math.max(MAX[left(root)], MAX[right(root)]);
				MIN[root] = Math.min(MIN[left(root)], MIN[right(root)]);
				SUM[root] = SUM[left(root)] + SUM[right(root)];
			}
		}

		public int getMax(int from, int to) {
			return getMax(1, 0, n - 1, from, to);
		}

		private int getMax(int root, int rl, int rr, int from, int to) {
			if (from > rr || to < rl || rl > rr) {
				return -1;
			}
			if (from == rl && to == rr) {
				return MAX[root];
			}
			int rm = (rr + rl) >> 1;
			int m1 = getMax(left(root), rl, rm, from, Math.min(to, rm));
			int m2 = getMax(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
			return Math.max(m1, m2);
		}

		public int getMin(int from, int to) {
			return getMin(1, 0, n - 1, from, to);
		}

		private int getMin(int root, int rl, int rr, int from, int to) {
			if (from > rr || to < rl || rl > rr) {
				return Integer.MAX_VALUE;
			}
			if (from == rl && to == rr) {
				return MIN[root];
			}
			int rm = (rr + rl) >> 1;
			int m1 = getMin(left(root), rl, rm, from, Math.min(to, rm));
			int m2 = getMin(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
			return Math.min(m1, m2);
		}

		public int getSum(int from, int to) {
			return getSum(1, 0, n - 1, from, to);
		}

		private int getSum(int root, int rl, int rr, int from, int to) {
			if (from > rr || to < rl || rl > rr) {
				return 0;
			}
			if (from == rl && to == rr) {
				return SUM[root];
			}
			int rm = (rr + rl) >> 1;
			int m1 = getSum(left(root), rl, rm, from, Math.min(to, rm));
			int m2 = getSum(right(root), rm + 1, rr, Math.max(from, rm + 1), to);
			return m1 + m2;
		}
	}

	private String lcs(String s1, String s2) {
		int n = s1.length();
		int m = s2.length();
		int[][] dp = new int[n + 1][m + 1];
		for (int i = 1; i <= n; i++) {
			for (int j = 1; j <= m; j++) {
				if (s1.charAt(i - 1) == s2.charAt(j - 1)) {
					dp[i][j] = dp[i - 1][j - 1] + 1;
				} else {
					dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
				}
			}
		}
		StringBuilder sb = new StringBuilder();
		int i = n;
		int j = m;
		while (i > 0 && j > 0) {
			if (s1.charAt(i - 1) == s2.charAt(j - 1)) {
				sb.append(s1.charAt(i - 1));
				i--;
				j--;
			} else {
				if (dp[i - 1][j] > dp[i][j - 1]) {
					i--;
				} else {
					j--;
				}
			}
		}
		return sb.reverse().toString();
	}

	private boolean isPrime(int n) {
		if (n <= 3)
			return n > 1;
		else if (n % 3 == 0 || n % 2 == 0)
			return false;
		for (long i = 5; i * i <= n; i += 6) {
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
		}
		return true;
	}

	private int[] getPrimes(int n) {
		int len = n + 1;
		boolean[] isPrimes = new boolean[len];
		int[] temps = new int[len];
		int index = 0;
		Arrays.fill(isPrimes, true);
		isPrimes[0] = isPrimes[1] = false;
		for (int i = 2; i * i < len; i++) {
			if (isPrimes[i]) {
				for (int j = i * i; j < len; j += i) {
					isPrimes[j] = false;
				}
			}
		}
		for (int i = 0; i < len; i++) {
			if (isPrimes[i])
				temps[index++] = i;
		}
		int[] primes = Arrays.copyOf(temps, index);
		return primes;
	}

	static void swap(char[] arrays, int pos1, int pos2) {
		char tmp = arrays[pos1];
		arrays[pos1] = arrays[pos2];
		arrays[pos2] = tmp;
	}

	static void swap(int[] arrays, int pos1, int pos2) {
		int tmp = arrays[pos1];
		arrays[pos1] = arrays[pos2];
		arrays[pos2] = tmp;
	}

	static long modPow(long n, long ex) {
		long res = 1;
		while (ex > 0) {
			if ((ex & 1) == 1)
				res = res * n % MOD;
			n = n * n % MOD;
			ex >>= 1;
		}
		return res;
	}

	static long ModInverse(long n) {
		return modPow(n, MOD - 2);
	}

	static long nCr(int n, int r) {
		if (r > n)
			return -1;
		// return (f[n] * ModInverse((f[r] * f[n - r]) % MOD)) % MOD;
		return 0;
	}
}

class Input {
	public BufferedReader reader;
	public StringTokenizer tokenizer;

	public Input(InputStream stream) {
		reader = new BufferedReader(new InputStreamReader(stream), 32768);
		tokenizer = null;
		tokenizer = null;
	}

	public String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}

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

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

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