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".
//------------------>>>>>>>>>>>>>>>> HI . HOW ARE YOU? <<<<<<<<<<<<<<<<<<<<<<<<<<<<<------------------------------

import java.util.*;
import java.math.*;
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;

//--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<-------------------

public class practice{
    static long[] count,count1,count2;
    static boolean[] prime;
    static int[] spf;
    static Node[] nodes,nodes1,nodes2;
    static long[] arr;
    static long[][] cost;
    static int[] arrInt,darrInt,farrInt;
    static long[][] dp;
    static char[] ch,ch1,ch2;
    static long[] darr,farr;
    static long[][] mat,mat1;
    static boolean[] vis;
    static long x,h;
    static long maxl,sum,total;
    static double dec;
    static long mx = (long)1e7;
    static long inf = (long)1e18;
    static String s,s1,s2,s3,s4;
    static long minl;
    static long mod = (long)1e9+7;
    // static int minl = -1;
    // static long n;
    static int n,n1,n2,q,r1,c1,r2,c2;
    static int arr_size = (int)2e5+10;
    static long a;
    static long b;
    static long c;
    static long d;
    static long y,z;
    static int m;
    static int ans;
    static long k;
    static FastScanner sc;
    static String[] str,str1;
    static Set<Long> set,set1,set2;
    static SortedSet<Long> ss;
    static List<Integer> list,list1,list2,list3;
    static PriorityQueue<Node> pq,pq1;
    static LinkedList<Node> ll,ll1,ll2;
    static Map<Integer,List<Integer>> map;
    static Map<Integer,Integer> map2;
    static Map<Integer,Node> map1;
    static StringBuilder sb,sb1,sb2;
    static int index;
    static int[] dx = {0,-1,0,1,-1,1,-1,1};
    static int[] dy = {-1,0,1,0,-1,-1,1,1};

    static class Node{
        int first;
        int second;
        Node(int f,int s){
            this.first = f;
            this.second = s;
        }
    }

    // public static void solve(){

    //    FastScanner sc = new FastScanner();
    //    int t = sc.nextInt();
    //    // int t = 1;
    //    for(int tt = 1 ; tt <= t ; tt++){


    //        System.out.println("Case #"+tt+": "+cost);

    //    }

    // }

    //--------------->>>>IF YOU ARE HERE FOR QUICKSORT HACK THEN SORRY NO HACK FOR YOU<<<--------------------

    public static void solve(){

        if(k == 1 || k > n || n == 1){
            System.out.println(power(m,n));
        }
        else if(n == k){
            System.out.println(power(m,(n+1)/2));
        }
        else if(k%2 == 1){
            System.out.println(power(m,2));
        }
        else{
            System.out.println(m);
        }

    }
    //----------->>>>>>> SPEED UP SPEED UP . THIS IS SPEEDFORCES . SPEED UP SPEEEEEEEEEEEEEEEEEEEEEEEEEEDDDDDD <<<<<<<------------------

    public static void main(String[] args) {

        sc = new FastScanner();
        // Scanner sc = new Scanner(System.in);
        // int t = sc.nextInt();
        int t = 1;
        // int l = 1;
        while(t > 0){

            // k = sc.nextLong();
            // x = sc.nextLong();
            // y = sc.nextLong();
            // z = sc.nextLong();

            // a = sc.nextLong();
            // b = sc.nextLong();
            // c = sc.nextLong();
            // d = sc.nextLong();

            // x = sc.nextLong();
            // y = sc.nextLong();
            // z = sc.nextLong();
            // d = sc.nextLong();

            n = sc.nextInt();

            // n1 = sc.nextInt();

            m = sc.nextInt();
            // q = sc.nextInt();

            // a = sc.nextLong();
            // b = sc.nextLong();

             k = sc.nextLong();

            // x = sc.nextLong();
            // d = sc.nextLong();

            // s = sc.next();

//                ch = sc.next().toCharArray();
            // ch1 = sc.next().toCharArray();

            // m = sc.nextInt();
            // n = 6;

            // arr = new long[n];
            // for(int i = 0 ; i < n ; i++){
            //     arr[i] = sc.nextLong();
            // }

            // arrInt = new int[n+1];
            // for(int i = 1 ; i <= n ; i++){
            //     arrInt[i] = sc.nextInt();
            // }

            // x = sc.nextLong();
            // y = sc.nextLong();
            // ch = sc.next().toCharArray();
            // m = n;
            // m = sc.nextInt();
            // darr = new long[m];
            // for(int i = 0 ; i < m ; i++){
            //     darr[i] = sc.nextLong();
            // }
            // k = sc.nextLong();
            // m = n;
            // darrInt = new int[n];
            // for(int i = 0 ; i < n ; i++){
            //     darrInt[i] = sc.nextInt();
            // }

            // farr = new long[m];
            // for(int i = 0 ; i < m ; i++){
            //     farr[i] = sc.nextLong();
            // }

            // farrInt = new int[m];
            // for(int i = 0; i < m ; i++){
            //     farrInt[i] = sc.nextInt();
            // }

            // m = n;
//            mat = new long[n][m];
//            for(int i = 0 ; i < n ; i++){
//                for(int j = 0 ; j < m ; j++){
//                    mat[i][j] = sc.nextLong();
//                }
//            }

            // m = n;
            // mat = new char[n][m];
            // for(int i = 0 ; i < n ; i++){
            //     String s = sc.next();
            //     for(int j = 0 ; j < m ; j++){
            //         mat[i][j] = s.charAt(j);
            //     }
            // }

            // str = new String[n];
            // for(int i = 0 ; i < n ; i++)
            //     str[i] = sc.next();

            // nodes = new Node[n];
            // for(int i = 0 ; i < n ;i++)
            //     nodes[i] = new Node(sc.nextInt(),i);

            solve();
            t -= 1;
        }

    }

    public static int log(double n,double base){

        if(n == 0 || n == 1)
            return 0;

        if(n == base)
            return 1;

        double num = Math.log(n);
        double den = Math.log(base);

        if(den == 0)
            return 0;

        return (int)(num/den);
    }

    public static boolean isPrime(long n) {
        // Corner cases
        if (n <= 1)
            return false;

        if (n <= 3)
            return true;

        // This is checked so that we can skip  
        // middle five numbers in below loop 
        if (n%2 == 0 || n%3 == 0)
            return false;

        for (int i=5; i*i<=n; i=i+6)
            if (n%i == 0 || n%(i+2) == 0)
                return false;

        return true;
    }

    public static void SpecialSieve(int MAXN)
    {
        spf = new int[MAXN];
        spf[1] = 1;
        for (int i=2; i<MAXN; i++)

            // marking smallest prime factor for every 
            // number to be itself. 
            spf[i] = i;

        // separately marking spf for every even 
        // number as 2 
        for (int i=4; i<MAXN; i+=2)
            spf[i] = 2;

        for (int i=3; i*i<MAXN; i++)
        {
            // checking if i is prime 
            if (spf[i] == i)
            {
                // marking SPF for all numbers divisible by i 
                for (int j=i*i; j<MAXN; j+=i)

                    // marking spf[j] if it is not  
                    // previously marked 
                    if (spf[j]==j)
                        spf[j] = i;
            }
        }
    }

    public static ArrayList<Integer> getFactorization(int x)
    {
        ArrayList<Integer> ret = new ArrayList<Integer>();
        while (x != 1)
        {
            ret.add(spf[x]);
            x = x / spf[x];
        }
        return ret;
    }


    public static long gcd(long a, long b)
    {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }

    public static long lcm(long a, long b)
    {
        return (b/gcd(b, a % b)) * a;
    }

    public static long mod_inverse(long a,long mod){
        long x1=1,x2=0;
        long p=mod,q,t;
        while(a%p!=0){
            q = a/p;
            t = x1-q*x2;
            x1=x2; x2=t;
            t=a%p;
            a=p; p=t;
        }
        return x2<0 ? x2+mod : x2;
    }

    public static void swapF(int[] curr,int l,int r){
        for(int i = l ; i < (r-l+1)/2 ; i++){
            swap(curr,i,r-i);
        }
    }

    public static void swap(int[] curr,int i,int j){
        int temp = curr[j];
        curr[j] = curr[i];
        curr[i] = temp;
    }

    static final Random random=new Random();

    static void ruffleSortLong(long[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            long temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSortInt(int[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            int temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static void ruffleSortChar(char[] a) {
        int n=a.length;//shuffle, then sort 
        for (int i=0; i<n; i++) {
            int oi=random.nextInt(n);
            char temp=a[oi];
            a[oi]=a[i]; a[i]=temp;
        }
        Arrays.sort(a);
    }

    static long binomialCoeff(long n, long k){

        long res = 1;

        // Since C(n, k) = C(n, n-k) 
        if (k > n - k)
            k = n - k;

        // Calculate value of 
        // [n * (n-1) *---* (n-k+1)] / [k * (k-1) *----* 1] 
        for (long i = 0; i < k; ++i) {
            res = (res*(n - i));
            res = (res/(i + 1));
        }

        return res;
    }

    static long mod(long x)
    {
        long y = mod;
        long result = x % y;
        if (result < 0)
        {
            result += y;
        }
        return result;
    }

    static long[] fact;

    public static long inv(long n){
        return power(n, mod-2);
    }

    public static void fact(int n){
        fact = new long[n+1];
        fact[0] = 1;
        for(int j = 1;j<=n;j++)
            fact[j] = (fact[j-1]*(long)j)%mod;
    }

    public static long binom(int n, int k){

        long prod = fact[n];
        prod*=inv(fact[n-k]);
        prod%=mod;
        prod*=inv(fact[k]);
        prod%=mod;
        return prod;
    }

    static long power(long x, long y){
        if (y == 0)
            return 1;
        if (y%2 == 1)
            return (x*power(x, y-1))%mod;
        return power((x*x)%mod, y/2)%mod;
    }

    public static long pow(long n,long p,long m){
        long  result = 1;
        if(p==0)
            return 1;

        while(p!=0)
        {
            if(p%2==1)
                result *= n;
            if(result>=m)
                result%=m;
            p >>=1;
            n*=n;
            if(n>=m)
                n%=m;
        }
        return result;
    }

    static void sieve(int n){

        prime = new boolean[n+1];
        for(int i=2;i<n;i++)
            prime[i] = true;

        for(int p = 2; p*p <=n; p++)
        {
            if(prime[p] == true)
            {
                for(int i = p*p; i <= n; i += p)
                    prime[i] = false;
            }
        }

    }

    static long abs(long a){
        return Math.abs(a);
    }

    static int abs(int a){
        return Math.abs(a);
    }

    static int max(int a,int b){
        if(a>b)
            return a;
        else
            return b;
    }
    static double max(double a,double b){
        if(a>b)
            return a;
        else
            return b;
    }
    static double min(double a,double b){
        if(a>b)
            return b;
        else
            return a;
    }

    static int min(int a,int b){
        if(a>b)
            return b;
        else
            return a;
    }

    static long max(long a,long b){
        if(a>b)
            return a;
        else
            return b;
    }

    static long min(long a,long b){
        if(a>b)
            return b;
        else
            return a;
    }

    static long sq(long num){
        return num*num;
    }

    static double sq(double num){
        return num*num;
    }

    static long sqrt(long num){
        return (long)Math.sqrt(num);
    }

    static double sqrt(double num){
        return Math.sqrt(num);
    }

    static class FastScanner {

        BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st=new StringTokenizer("");
        String next() {
            while (!st.hasMoreTokens())
                try {
                    st=new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
        int[] readArray(int n) {
            int[] a=new int[n];
            for (int i=0; i<n; i++) a[i]=nextInt();
            return a;
        }
        long nextLong() {
            return Long.parseLong(next());
        }
    }

}