On his free time, Chouti likes doing some housework. He has got one new task, paint some bricks in the yard.

There are n bricks lined in a row on the ground. Chouti has got m paint buckets of different colors at hand, so he painted each brick in one of those m colors.

Having finished painting all bricks, Chouti was satisfied. He stood back and decided to find something fun with these bricks. After some counting, he found there are k bricks with a color different from the color of the brick on its left (the first brick is not counted, for sure).

So as usual, he needs your help in counting how many ways could he paint the bricks. Two ways of painting bricks are different if there is at least one brick painted in different colors in these two ways. Because the answer might be quite big, you only need to output the number of ways modulo 998 244 353.

Input

The first and only line contains three integers n, m and k (1 ≤ n,m ≤ 2000, 0 ≤ k ≤ n-1) — the number of bricks, the number of colors, and the number of bricks, such that its color differs from the color of brick to the left of it.

Output

Print one integer — the number of ways to color bricks modulo 998 244 353.

Examples

Input


3 3 0


Output


3


Input


3 2 1


Output


4

Note

In the first example, since k=0, the color of every brick should be the same, so there will be exactly m=3 ways to color the bricks.

In the second example, suppose the two colors in the buckets are yellow and lime, the following image shows all 4 possible colorings.

<image>
import java.util.*; 
import java.math.*;
import java.io.*;
import java.text.DecimalFormat;
import java.math.BigInteger;
public class Main{
    //static int d=20;
    static long mod=1000000007 ;
    
    static ArrayList<ArrayList<Integer>> arr;
   // static long[] dp1,dp2;
    static int[] a;
    static int[][][] vis;
    static long max;
    static HashSet<String> hs;
    static int flag,ans;
    static long max1,max2,ans1;
    
    static int total,possible=0;
    static int[] tin,tout,parent,level;
    static int[][] reach;
    static HashMap<Long,Integer> hm;
    static long[] dp1,dp2,dp3,dp4;
    static int[] c ;
       
    public static void main(String[] args)  throws IOException {
        ///long start=System.currentTimeMillis();
        boolean online = false  ;
        String fileName = "A-small-attempt0 (1).in";
        PrintWriter out; 
        if (online) {
            s.init(new FileInputStream(new File("Downloads/"+fileName)));
             out= new PrintWriter(new FileWriter(fileName + "out.txt"));
        }
         else {
            s.init(System.in);   
        
            out = new PrintWriter(new BufferedWriter(new OutputStreamWriter(System.out)));
        }
        int n=s.ni();
        int m=s.ni();
        int k=s.ni();
        long mod = 998244353;
        long[][] dp=new long[n][k+1];
        // for(int i=0;i<n;i++){
        //     Arrays.fill(dp[i],-1);
        // }
        dp[0][0]=m;
        for(int i=0;i<n;i++){
            for(int j=0;j<=k;j++){
                if(dp[i][j]!=0 && (i+1)<n){
                    dp[i+1][j] =(dp[i+1][j]+ dp[i][j])%mod;
                    if(j+1<=k){
                        dp[i+1][j+1] =(dp[i+1][j+1] + (dp[i][j]*(m-1))%mod)%mod;
                    }
                }

            }
        }
        out.println(dp[n-1][k]);
        out.close();      
            

    }

    public static boolean mazedfs(int[] c, int[]a, int[] b, int flag, int index){
        int n=c.length-1;
        if(index==n)
            return true;
        for(int i=index;i<n;i++){
            if(a[i]==b[i])
                continue;
            if(a[i]<b[i])
                return false;

            boolean currentFlag=true;
            for(int u=0;u<=3;u++){
                for(int v=0;v<=3;v++){
                    if((u|v)!=a[i] )
                        continue;
                    if((u&v)!=b[i])
                        continue;

                    if(c[i]==-1 && c[i+1]==-1){
                c[i]=u;
                c[i+1]=v;
                if(!mazedfs(c, a,b,flag,index+1)){
                    c[i]=v;
                    c[i+1]=u;
                    if(mazedfs(c, a,b,flag,index+1))
                        return true;
                    else
                        currentFlag=false;

                }
                else
                    return true;
                c[i]=c[i+1]=-1;

            }
            else if(c[i]!=-1 && c[i+1]!=-1){
                    if((c[i]|c[i+1])!=a[i]){
                        flag=1;
                        return false;
                    }
                    if((c[i] & c[i+1]) !=b[i]){
                        flag=1;
                        return false;
                    }
                }
                else{
                    if(c[i]!=-1){
                        int store=c[i];
                        if(c[i]==u){
                            c[i+1]=v;
                        }
                        else if(c[i]==v){
                            c[i+1]=u;
                        }
                        else{
                            flag=1;
                            currentFlag=false;
                        }
                        if(mazedfs(c, a,b,flag,index+1))
                            return true;
                        
                        c[i]=store;
                        c[i+1]=-1;

                    }
                    else if(c[i+1]!=-1){
                        int store=c[i+1];
                        if(c[i+1]==u){
                            c[i]=v;
                        }
                        else if(c[i+1]==v){
                            c[i]=u;
                        }
                        else{
                            flag=1;
                            currentFlag=false;
                        }
                         if(mazedfs(c, a,b,flag,index+1))
                            return true;
                        c[i+1]=store;
                        c[i]=-1;

                    }
                }
                }
            }

            if(currentFlag==false)
                return false;
            
            }
        return true;

    }
   
    

    public static void union(int[] a,int x,int y){
        int u=find(a,x);
        int v=find(a,y);
        a[v]=u;

    }
    public static int find(int[] a,int x){
        if(a[x]!=x){
            a[x]=find(a,a[x]);
        }
        return a[x];
    }
    public static int gcd(int a, int b){
            if (a == 0) return b;
            return gcd(b % a, a);
    }
        
    public static void cfs(ArrayList<HashSet<Integer>> arr,int c,int p,int g,int[] vis){
        vis[c]=1;
        if(g!=-1){
            if(!arr.get(c).contains(g)){
                flag=1;
                return;
            }
        }
        for(int x:arr.get(c)){
            if(x!=p && x!=g && vis[x]==0 ){
                cfs(arr,x,c,p,vis);
            }
        }

    }
                          //   public static void dfs(int u,int p){
//                            //       if(p>=0)
//                            //           tin[u]=tout[u]=tt++;
//                            //       if(p>=0)
//                            //           level[u]=level[p]+1;
//                            //       parent[u]=p;
//                            //       for(int x:arr.get(u)){
//                            //           if(x!=p){
//                            //               dfs(x,u);
//                            //               tout[u]=Math.max(tout[u],tout[x]);
//                            //           }
//                            //       }
//                            //       
//
//
 //   }
    public static int lca(int[][] p,int a,int b){
        if(level[a]<level[b]){
            int x=a;
            a=b;
            b=x;
        }
        int log=p[0].length;
        for(int i=log-1;i>=0;i--){
            if(1<<i<=level[a]-level[b]){
                a=p[a][i];
            }
        }
        if(a==b)
            return a;
        for(int i=log-1;i>=0;i--){
            if(p[a][i]!=p[b][i]){
                a=p[a][i];
                b=p[b][i];
            }
        }
        return p[a][0];

    }
    public static int[][] par(int[] parent){
        int n=arr.size();
        int[][] p=new int[n][17];
        for(int i=0;i<n;i++)
            p[i][0]=parent[i];
        for(int k=1;k<17;k++){
            for(int i=0;i<n;i++){
                if(p[i][k-1]>-1)
                    p[i][k]=p[p[i][k-1]][k-1];
                else
                    p[i][k]=-1;
            }
        }
        return p;
    }
    static class Edge implements Comparable<Edge>{
           int from;
            int to;
            long cost;
    
           public Edge(int from, int to, long weight) {
               this.from = from;
               this.to = to;
               this.cost= weight;
           }
           public int compareTo(Edge o){
                return (int)Math.signum(cost-o.cost); 
           }

    }                               
    static class Node {
        int start;
        int end;

        int cost;
        int updated;

        Node[] nodes;

        public Node(int start, int end) {
            this.start = start;
            this.end = end;

            if (start < end) {
                int[] pos = {start, (start + end) / 2, end};
                nodes = new Node[2];
                for (int i = 0; i < 2; i++) {
                    nodes[i] = new Node(pos[i] + i, pos[i + 1]);
                }
            }
        }

        public void update(int queryStart, int queryEnd, int value) {
            if (queryEnd < start || end < queryStart) {
                return;
            }

            if (queryStart <= start && end <= queryEnd) {
                cost += value;
                updated += value;
                return;
            }

            propagate();
            for (Node node: nodes) {
                node.update(queryStart, queryEnd, value);
            }
        }

        public int query(int pos) {
            if (pos < start || end < pos) {
                return 0;
            }

            if (start == end) {
                return cost;
            }

            propagate();
            int ans = 0;
            for (Node node: nodes) {
                ans = Math.max(ans, node.query(pos));
            }
            return ans;
        }

        public void propagate() {
            if (updated != 0 && start < end) {
                for (Node node: nodes) {
                    node.cost += updated;
                    node.updated += updated;
                }
                updated = 0;
            }
        }
    }
    public static double nthroot(int n, double A) {
        return nthroot(n, A, 0.0000001);
    }
    public static double nthroot(int n, double A, double p) {
        if(A < 0) {
            System.err.println("A < 0");// we handle only real positive numbers
            return -1;
        } else if(A == 0) {
            return 0;
        }
        double x_prev = A;
        double x = A / n;  // starting "guessed" value...
        while(Math.abs(x - x_prev) > p) {
            x_prev = x;
            x = ((n - 1.0) * x + A / Math.pow(x, n - 1.0)) / n;
        }
        return x;
    }
    
    static class item implements Comparable<item> {
        int from,to,cost;
        public item(int x,int y){
            from=x;
            to=y;
            
        }
        public int compareTo(item o){
            
            return  o.cost-cost;
        }
        
    }
   
    public static void dfs2(int c,int p,int[] a){
        //System.out.println(c+" "+p);
       
        
        

    }
//public static void dfs(int x,int[] vis,Stack<Integer> st){
    //    vis[x]=1;
    //    ArrayList<Integer> arr2=arr.get(x);
    //    Collections.sort(arr2);
    //    for(int i=arr2.size()-1;i>=0;i--){
    //        int z=arr2.get(i);
    //        if(vis[z]==0)
    //            dfs(z,vis,st);
    //    }
    //    st.push(x);
//
    //}
    public static long gcd2(long a, long b){
            if (a == 0) return b;
            return gcd2(b % a, a);
    }
        
    public static boolean check(long x){
        if(x%4==0 || x%7==0 || x%11==0)
            return true;
        if(x<4 || x<7 || x<11)
            return false;
        if(x%2==0){
            return check(x/2);
        }
        else
            return check(x/2) && check((x+1)/2);
    }
    public static int angle(int x1,int x2,int x3,int y1,int y2,int y3){
        long val=(y2-y1)*1L*(x3-x2)-(y3-y2)*1L*(x2-x1);
        if(val<0)
            return 1;
        else if(val>0)
            return -1;
        else
            return 0;
    }
    
    static class BIT{
    
        int N;
        long tree[];
        
        BIT(int N){
            this.N = N;
            tree = new long[N + 1];
        }
        
        void update(int idx,long val){
            while(idx <= N){
                tree[idx]+=val;
                idx += (idx & -idx);
            }
        }
        
        long query(int l,int r){
            if(l == 1)
                return read(r);
            else
                return read(r) - read(l-1);
        }
        
        long read(int idx){
            long sum = 0;
            while(idx > 0){
                sum += tree[idx];
                idx -= (idx & -idx);
            }
            return sum;
        }
    }
    public static boolean pal(String a){
        int i=0;
        int j=a.length()-1;
        while(i<j){
            if(a.charAt(i)!=a.charAt(j)){
                return false;
            }
            i++;
            j--;
        }
        return true;
            
    }
    public static long find(long n,long k){
        if(n==2){
            if(k==1 || k==3)
                return 1;
            else
                return 2;
        }
        long t=pow2(2,n,mod)-1;
        long z=(t+1)/2;
        if(k==z)
            return n;
        if(k<z)
            return find(n-1,k);
        else
            return find(n-1,k-z);
    }
    public static long pow2(long a,long b,long mod){
            
            long ans=1;
           // long z=b;
            while(b>0){
               
                if(b%2==1)
                    ans=(a*ans)%mod;
                a=(a*a)%mod;
                b/=2;
            }
          
            return  ans;
    }
     public static long pow3(long a,long b){
            
            long ans=1;
           // long z=b;
            while(b>0){
               
                if(b%2==1)
                    ans=(a*ans);
                a=(a*a);
                b/=2;
            }
          
            return  ans;
    }
    public static long fib(long n){
        long[][]    f=new long[][]{{1L,1L},{1L,0}};
        if(n==0)
            return 0;
        f=arrpow(f,n-1);
        return f[0][0];
    }
    public static long[][] arrpow(long[][] a,long b){
       
            int n=a.length;
          //  long z=b;
            long[][] ans=new long[n][n];
            for(int i=0;i<n;i++)
                ans[i][i]=1L;
            while(b>0){
                
                if(b%2==1)
                    ans=mul(a,ans);
                a=mul(a,a);
                b/=2;
            }
            
            return  ans;
    }
    public static long[][] mul(long[][] a,long[][] b){
        int n=a.length;
        int m=b[0].length;
        long[][] ans=new long[n][m];
        if(n==2 && m==2 && b.length==2){
            ans[0][0]=((a[0][0]*b[0][0])%mod+(a[0][1]*b[1][0]))%mod;
            ans[0][1]=((a[0][0]*b[0][1])%mod+(a[0][1]*b[1][1]))%mod;
            ans[1][0]=((a[1][0]*b[0][0])%mod+(a[1][1]*b[1][0]))%mod;
            ans[1][1]=((a[1][1]*b[1][1])%mod+(a[1][0]*b[0][1]))%mod;
            return ans;

        }
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                for(int k=0;k<b.length;k++){
                    ans[i][j]=(ans[i][j]+(a[i][k]*b[k][j])%mod)%mod;
                }
            }
        }
        return ans; 
    }
     static class name implements Comparable<name> {
        long l,b,h;
        public name(long   x,long y,long z){
            {
                l=x;
                b=y;        
            }
            
            
            h=z;
        }
        public int compareTo(name o){
            return -(int)(l*b-o.l*o.b);
        }
        
    }
    public static class s {
        static BufferedReader reader;
        static StringTokenizer tokenizer;
    
        /** call this method to initialize reader for InputStream */
        static void init(InputStream input) {
            reader = new BufferedReader(
                        new InputStreamReader(input) );
            tokenizer = new StringTokenizer("");
        }   
    
        /** get next word */
        static String ns() throws IOException {
            while ( ! tokenizer.hasMoreTokens() ) {
                //TODO add check for eof if necessary
                tokenizer = new StringTokenizer(
                    reader.readLine() );
            }
            return tokenizer.nextToken();
        }
    
        static int ni() throws IOException {
            return Integer.parseInt( ns() );
        }
    
        static double nd() throws IOException {
            return Double.parseDouble( ns() );
        }
        static long nl() throws IOException {
            return Long.parseLong( ns() );
        }
    }
}   
