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".

//package cf;
import java.io.*;
import java.util.*;
import java.util.jar.JarOutputStream;

public class T_class {
    static int p=1000000007;
    static int max=(int)1e5;
    static List<Integer> l1=new ArrayList<>();
    static boolean prime[]=new boolean[max];
    static long fact[]=new long[3_000_00];
    static class  pr_int
    {
        int first;
        int second;
        public pr_int(int first, int second) {
            this.first = first;
            this.second = second;
        }
    }
    static  class edge
    {
        int v,w,lst;
        edge(int v,int w)
        {
            this.v=v;
            this.w=w;
        }
    }
    static  class wt
    {
        int n,d,s;

        public wt(int n, int d, int s) {
            this.n = n;
            this.d = d;
            this.s = s;
        }
    }
    static  long anss=0;
    public static void main(String[] args) throws Exception {
        BufferedWriter out = new BufferedWriter(new OutputStreamWriter(new FileOutputStream(java.io.FileDescriptor.out), "ASCII"), 512);
        FastReader sc = new FastReader();
        int t =1;//sc.nextInt();
        StringBuilder sb2 = new StringBuilder();
        while (t-- >0)
        {

            int n=sc.nextInt();
            int m=sc.nextInt();
            int k=sc.nextInt();
            int p[]=new int[n+2];
            int r[]=new int[n+2];
            for(int i=0;i<=n;i++)
            {
                p[i]=i;
                r[i]=1;
            }
            for(int i=0;i<=(n-k);i++)
            {
                for(int j=0;j<k/2;j++)
                {
                    union(i+j,i+k-j-1,p,r);
           //         System.out.println((i+j)+"  "+(i+k-j-1));
                }
            }
         //   System.out.println(Arrays.toString(p));
            long ans=1;
            for(int i=0;i<n;i++)

            {
                if(p[i]==i)
                {
                    ans=(ans*(long) m)%mod;
                }
            }
            sb2.append(ans);
        }
        System.out.println(sb2.toString());
        out.flush();

    }
    static void sortMyMapusingValues(HashMap<Integer, Integer> hm) {
        List<Map.Entry<Integer, Integer>> capitalList = new LinkedList<>(hm.entrySet());

        Collections.sort(capitalList, new Comparator<Map.Entry<Integer, Integer>>() {
            public int compare(Map.Entry<Integer, Integer> o1, Map.Entry<Integer, Integer> o2) {
                return (o1.getValue()).compareTo(o2.getValue());
            }
        });
        HashMap<Integer, Integer> result = new HashMap<>();
        for (Map.Entry<Integer, Integer> entry : capitalList) {
            result.put(entry.getKey(), entry.getValue());
        }
    }
    static class BIT {
        long[] tree;
        public BIT(int size) {
            tree = new long[size + 1];
        }
        public long sum(int i) {
            long ans = 0;
            while (i > 0) {
                ans += tree[i];
                i -= i & -i;
            }
            return ans;
        }

        public long query(int i, int j) {
            return sum(j) - sum(i - 1);
        }

        public void add(int i, long val) {
            while (i < tree.length) {
                tree[i] += val;
                i += i & -i;
            }
        }

        public void set(int i, long val) {
            add(i, val - query(i, i));
        }
    }

    static long lcm(long a,long b)
    {
        return  a*b/gcd(a,b);
    }
    static boolean done=false;
    static long ret;
    public  static long tolong(char ar[])
    {
        long ans=0;
        for(char i:ar)
            ans=ans*10+ (i-'0');

        return ans;
    }
    public  static  void recur(char ar[],int n,int cur,long lcm,boolean con)
    {
        if(cur==n)
        {
            System.out.println(tolong(ar)+" "+lcm);
            done=tolong(ar)%lcm==0;
            if(done)
                ret=tolong(ar);
            return;
        }
        int lst=ar[cur]-'0';
        for(int i=con?ar[cur]-'0':0;i<=9;i++)
        {
            char prev=ar[cur];
            ar[cur]=(char) (i+'0');
            recur(ar, n, cur + 1, i==0?lcm:lcm(i,lcm),lst==i);
            ar[cur]=prev;
            if(done)
                return ;
        }
    }
    static long ansa(long l,long r,long s,long ss,int n,int ar[])
    {

        while(l<=r)
        {
            long mid=(l+r)/2;
            long tot=0;
            for(int i=0;i<n;i++)
            {
                tot+=Math.abs(ar[i]-mid);
            }

            if(tot*2<=s)
            {
                // System.out.println(s+" - "+(mid*n)+" <= "+ss);
                return mid;
            }
            else if(tot*2>s)
            {
                r=mid-1;
            }
            else
            {
                l=mid+1;
            }
        }
        return 1;
    }
    static void ruffle_sort(long[] a) {
        //shandom_ruffle
        Random r=new Random();
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=Math.abs(r.nextInt(i+1));
            long temp=a[i];
            a[i]=a[oi];
            a[oi]=temp;
        }

        //sort
        Arrays.sort(a);
    }
    static void ruffle_sort(int[] a) {
        //shandom_ruffle
        Random r=new Random();
        int n=a.length;
        for (int i=0; i<n; i++) {
            int oi=Math.abs(r.nextInt(i+1));
            int temp=a[i];
            a[i]=a[oi];
            a[oi]=temp;
        }

        //sort
        Arrays.sort(a);
    }
    static long mod=(long) 1e9+7;
    private static long nC2(long n) {
        return n*(n-1)/2;
    }
    static long mul(long a, long b) {
        return a*b%mod;
    }

    static long add(long a, long b) {
        return (a+b)%mod;
    }
    static void precomp() {
        fact[0]=1;
        for (int i=1; i<fact.length; i++) fact[i]=mul(fact[i-1], i);
    }
    static long modInv(long x) {
        return pow(x, mod-2,mod);
    }
    static long nCk(int n, int k) {
        return mul(fact[n], mul(modInv(fact[k]), modInv(fact[n-k])));
    }


    private static List<Long> getdivisors(long n) {
        List<Long> l1=new ArrayList<>();
        for(long i=1;i<=Math.sqrt(n);i++)
        {
            if(n%i==0){
                l1.add(i);
                if(n/i!=i)
                    l1.add(n/i);
            }
        }
        // System.out.println(l1);
        Collections.sort(l1);
        return l1;
    }

    private static int count(int k, int l, String cur) {
        char ar[]=cur.toCharArray();
        int c=0;
        for(int i=k;i<=l;i++)
        {
            if(i=='1')
                c++;
        }
        return c;
    }

    private static String revese(String substring) {
        StringBuilder sb=new StringBuilder();
        sb.append(substring);
        sb=sb.reverse();
        return sb.toString();
    }


    static  int ht[]=new int[max];
    /*static class BIT {
        long[] tree;
        public BIT(int size) {
            tree = new long[size + 1];
        }
        public long sum(int i) {
            long ans = 0;
            while (i > 0) {
                ans += tree[i];
                i -= i & -i;
            }
            return ans;
        }

        public long query(int i, int j) {
            return sum(j) - sum(i - 1);
        }

        public void add(int i, long val) {
            while (i < tree.length) {
                tree[i] += val;
                i += i & -i;
            }
        }

        public void set(int i, long val) {
            add(i, val - query(i, i));
        }
    }
    */public static long pow(long a,long b,long m)
    {
        long r=1;
        while(b!=1)
        {
            if(b%2!=0)
                r=(r*a)%m;
            b=b>>1;
            a=(a*a)%m;
        }
        return (r*a)%m;
    }
    /*public static long gcd(long a,long b)
    {
        if(b>a)
        {
            a=a^b;
            b=a^b;
            a=a^b;
        }
        if(b==0)
            return a;
        return gcd(b,a%b);
    }*/
    static long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
    public static void extgcd(long a,long b)
    {/*
            if(a==0)
            {
                x=0;
                y=1;
                d=b;
                // return ;
            }
            else
            {

                extgcd(b%a,a);

                long t=y;
                y=x;
                x=t-(b/a)*x;
            }*/
    }
    static  Set<Integer > used=new HashSet<>();
    public static void dfs(List<Integer>[] adj, int u, int p, boolean[] vis,long ind[],long n)
    {
        // anss-=((ind[u]-1)*(ind[u]-2))/2>0&&!used.contains(u)?((ind[u]-1)*(ind[u]-2))/2:0;

        if(((ind[u]-1)*(ind[u]-2))/2>0)
        {
            //   System.out.println(u+" -- "+((ind[u]-1)*(ind[u]))/2);
            //   used.add(u);
        }
        vis[u]=true;
        int c=0;
        for(int v:adj[u])
        {
            if(v!=p&&vis[v])
            {
                //   System.out.println(u+" c--c"+v+" "+((ind[v]-1)*(ind[v]))/2);
                if(((ind[v]-1)*(ind[v]-2))/2>0) {
                    anss -= ((ind[v] - 1) * (ind[v] - 2)) / 2 > 0 && !used.contains(v) ? ((ind[v] - 1) * (ind[v] - 2)) / 2 : 0;
                    used.add(v);
                }
                if(((ind[u]-1)*(ind[u]-2))/2>0) {
                    anss -= ((ind[u] - 1) * (ind[u] - 2)) / 2 > 0 && !used.contains(u) ? ((ind[u] - 1) * (ind[u] - 2)) / 2 : 0;
                    used.add(u);
                }
                continue;
            }
            if(!vis[v])
            {
                c++;
                dfs(adj,v,u, vis,ind,n+1);
            }
        }
        if(c==0)
        {
            anss+=(n)*(n+1l)/2;
        }
        vis[u]=false;
    }
    public static void seive()
    {
        for(int i=0;i<max;i++)
            prime[i] = true;

        for(int p = 2; p*p <=max; p++)
        {
            // If prime[p] is not changed, then it is a prime
            if(prime[p] == true)
            {
                // Update all multiples of p
                for(int i = p*p; i <=max; i += p)
                    prime[i] = false;
            }
        }

        // Print all prime numbers
        for(int i = 2; i <= max; i++)
        {
            if(prime[i] == true)
            {
                l1.add(i);
            }
        }
    }
    public static boolean union(int a, int b, int p[], int r[]){
        // add your code here
        int pa=find(a,p,r);
        int pb=find(b,p,r);
        if(pa==pb)
            return true;
        if(pa!=pb)
        {
            if(r[pa]<r[pb])
            {
                p[pa]=pb;
            }
            else if(r[pa]>r[pb])
            {
                p[pb]=pa;
            }
            else
            {
                p[pa]=pb;
                r[pb]++;
            }
        }
        return false;
    }
    public static int find(int x,int p[],int r[])
    {
        if(p[x]==x)
            return x;
        p[x]=find(p[x],p,r);
        return p[x];
    }
    public static int binary_Search_upper(int[] ar,int l, int x)
    {
        int res=-1;
        int r=ar.length-1;
        while(l<=r)
        {
            int mid=(l+r)>>1;
            if(ar[mid]<=x)
            {
                res=mid;
                l=mid+1;
            }
            else if(ar[mid]>x)
            {
                //res=mid;
                r=mid-1;
            }
        }
        return res;
    }
    public static int binary_Search_lower(long[] ar, long x)
    {
        int res=ar.length;
        int l=0;int r=ar.length-1;
        while(l<=r)
        {
            int mid=(l+r)>>1;
            if(ar[mid]>=x)
            {
                res=mid;
                r=mid-1;
            }
            else
            {
                l=mid+1;
            }
        }
        return res;
    }
    int bit[]=new int[(int)1e6];
    public void update(int n,int val,int i)
    {
        i++;
        while(i<n)
        {
            bit[i]+=val;
            i+=(i)&(-i);
        }

    }
    public long query(int n,int i)
    {
        i++;
        long sum=0;
        while(i>0)
        {
            sum+=bit[i];
            i-=(i)&(-i);
        }
        return sum;
    }


    ///////////////////////////////////////////////////////////////////////////////////
    //////////////////////////////////////////////////////////////////////////////////////////////
    static class FastReader {

        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }


}
