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.util.*;
import java.io.*;
import java.math.*;
import static java.lang.Math.*;

public class Main{

    int ApowBmodC(long a, long b, long c){
        if(b==0) return 1;
        long ret = ApowBmodC(a*a%c, b/2, c);
        if((b&1) != 0)
            ret = ret*a%c;
        return (int)ret;
    }
    
    public void go(){
        int n=sc.nextInt(), m=sc.nextInt(), k=sc.nextInt(), ret;
        if(k==1 || k>n)
            ret = ApowBmodC(m, n, INF);
        else if(k==n)
            ret = ApowBmodC(m, (n+1)/2, INF);
        else if((k&1)==0)
            ret = m;
        else
            ret = ApowBmodC(m, 2, INF);

        System.out.printf("%d\n", ret);
    }

    // syntax
    // ArrayList<Integer>[] myMat = (ArrayList<Integer>[]) new ArrayList[nB];

    // Pairs
    public class ii implements Comparable< ii >{
        int x, y;
        public ii(){}
        public ii(int xx, int yy){ x=xx; y=yy; }
        public int compareTo(ii p){ return x!=p.x ? x-p.x : y-p.y; }
        public int hashCode(){ return 31*x+y; }
        public boolean equals(Object o){
            if(!(o instanceof ii)) return false;
            ii p = (ii) o;
            return x==p.x && y==p.y;
        }
        public String toString(){ return "("+x+", "+y+")"; }
    }
/*
    public class pair< X extends Comparable< X >,Y extends Comparable< Y > > implements Comparable< pair< X,Y > >{
        X x;
        Y y;
        public pair(){}
        public pair(X xx, Y yy){ x=xx; y=yy; }
        public int compareTo(pair< X,Y > p){ return x.compareTo(p.x)!=0 ? x.compareTo(p.x) : y.compareTo(p.y); }
        public int hashCode(){ return 31*x.hashCode()+y.hashCode(); }
        public boolean equals(Object o){
            if((o.getClass() != this.getClass())) return false;
            pair< X,Y > p = (pair< X,Y >) o;
            return x.equals(p.x) && y.equals(p.y);
        }
        public String toString(){ return "("+x+", "+y+")"; }
    }
*/
    // my stuff
    public static final int INF = 1000*1000*1000+7;
    public static final double EPS = 1e-9;
    public static final double PI = 2*acos(0.0);
    public void rev(Object[] a){ for(int i=0; i<a.length/2; ++i){ Object t=a[i]; a[i]=a[a.length-1-i]; a[a.length-1-i]=t; } }
    public void rev(int[] a){ for(int i=0; i<a.length/2; ++i){ int t=a[i]; a[i]=a[a.length-1-i]; a[a.length-1-i]=t; } }
    public int bit_count(long x){ return x==0 ? 0 : 1+bit_count(x&(x-1)); }
    public int low_bit(int x){ return x&-x; } // 0011 0100 returns 0000 0100
    public int sign(int x){ return x<0 ? -1 : x>0 ? 1 : 0; }
    public int sign(double x){ return x<-EPS ? -1 : x>EPS ? 1 : 0; }
    int[] unpack(ArrayList< Integer > a){
        int[] ret = new int[a.size()];
        for(int i=0; i<a.size(); ++i) ret[i] = a.get(i);
        return ret;
    }

    // generic main stuff
    static myScanner sc;
    static PrintWriter pw;
    static long startTime;
    public static void main(String[] args) throws Exception{
        // sc = new Scanner(System.in);
        sc = (new Main()).new myScanner(new BufferedReader(new InputStreamReader(System.in)));
        pw = new PrintWriter(System.out);
        startTime = System.nanoTime();
        (new Main()).go();
        // errprintln("nanoTime="+(System.nanoTime()-startTime)/1000000/1000.0);
        pw.flush();
        System.exit(0);
    }

    // capable of reading   2.86M 6dp doubles per second
    //                      2.16M 12dp doubles per second
    //                      2.75M int per second
    public class myScanner{
        private BufferedReader f;
        private StringTokenizer st;
        public myScanner(BufferedReader ff){ f=ff; st=new StringTokenizer(""); }
        public int nextInt(){ return Integer.parseInt(nextToken()); }
        public double nextDouble(){ return Double.parseDouble(nextToken()); }
        public String nextLine(){
            st=new StringTokenizer("");
            String ret="";
            try{ ret=f.readLine(); }catch(Exception e){}
            return ret;
        }
        public String nextToken(){
            while(!st.hasMoreTokens()) try{ st=new StringTokenizer(f.readLine()); } catch(Exception e){}
            return st.nextToken();
        }
    }


}
