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.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.OutputStream;
import java.io.OutputStreamWriter;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;
import java.util.Set;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeSet;

public class q5 {

	 public static int gcd(int a,int b) {
		 if(b==0) return a;
		 else return gcd(b,a%b);
	 }
	 
	 // Credits to GFG
	 static public int dfs(ArrayList<Integer>[] graph,ArrayList<Integer> arr, int start, int[] visited) {
		 visited[start]=1;
		 boolean leaf=true;
		 int ans=0;
		 int totalchild=0;
		 for(int i:graph[start]) {
			 if(visited[i]==0) {
				 ans+=q5.dfs(graph, arr, i, visited);
				 leaf=false;
			 }
		 }
		 if(leaf) ans=1;
		 arr.add(ans);
		 return ans;
		 
	 }
	 
	 
	  
	  
	
	
	 
	
	 
	 
	public static void main(String[] args) throws IOException {
		// TODO Auto-generated method stub
		// Editorial implementation for practice
		Reader.init(System.in);
		StringBuffer output=new StringBuffer("");
		PrintWriter out=new PrintWriter(System.out);
		int n=Reader.nextInt();
		int m=Reader.nextInt();
		int k=Reader.nextInt();
		long[][] dp=new long[n+1][n+1];
		dp[0][0]=m;
		long mod=998244353;
		for(int i=1;i<n;i++) {
			dp[i][0]=dp[i-1][0];
			for(int kk=1;kk<=n;kk++) {
				dp[i][kk]=dp[i-1][kk]+dp[i-1][kk-1]*(m-1);
				dp[i][kk]%=mod;
			}
		}
		output.append(dp[n-1][k]);
		out.write(output.toString());
		out.flush();
	}
}

 
class Node2{
	String name;
	double ft,st;
	Node2(String a,double b,double c){
		name=a;
		ft=b;
		st=c;
	}
	
}

class Heap{
	int[] mylist;
	int[] mymap;
	int[] vtxmymap;
	int size;
	long[] update;
	long updatevalue;
	int[] removed;
	Heap(int[] graph){
		int l=graph.length;
		updatevalue=0;
		removed=new int[l];
		update=new long[l];
		size=l-1;
		mylist=new int[l];
		mymap=new int[l];
		vtxmymap=new int[l];
		for(int i=size;i>0;i--) {
			if(i>size/2) {
				mylist[i]=graph[i];
				mymap[i]=i;
				vtxmymap[i]=i;
			}
			else {
				mylist[i]=graph[i];
				mymap[i]=i;
				vtxmymap[i]=i;
				boolean end=false;
				int parent=i;
				while(!end) {
					int leftchild=2*parent;
					int rightchild=2*parent+1;
					if(leftchild>size) {
						end=true;
					}
					else if(rightchild>size) {
						if(mylist[leftchild]<mylist[parent]) {
							int parentNode=vtxmymap[parent];
							int childNode=vtxmymap[leftchild];
							int parentDeg=mylist[parent];
							int childDeg=mylist[leftchild];
							mylist[parent]=childDeg;
							mylist[leftchild]=parentDeg;
							mymap[parentNode]=leftchild;
							mymap[childNode]=parent;
							vtxmymap[parent]=childNode;
							vtxmymap[leftchild]=parentNode;
							parent=leftchild;
						}
						else end=true;
					}
					else {
						if(mylist[leftchild]<=mylist[rightchild]) {
							if(mylist[leftchild]<mylist[parent]) {
								int parentNode=vtxmymap[parent];
								int childNode=vtxmymap[leftchild];
								int parentDeg=mylist[parent];
								int childDeg=mylist[leftchild];
								mylist[parent]=childDeg;
								mylist[leftchild]=parentDeg;
								mymap[parentNode]=leftchild;
								mymap[childNode]=parent;
								vtxmymap[parent]=childNode;
								vtxmymap[leftchild]=parentNode;
								parent=leftchild;
							}
							else end=true;
						}
						else {
							if(mylist[rightchild]<mylist[parent]) {
								int parentNode=vtxmymap[parent];
								int childNode=vtxmymap[rightchild];
								int parentDeg=mylist[parent];
								int childDeg=mylist[rightchild];
								mylist[parent]=childDeg;
								mylist[rightchild]=parentDeg;
								mymap[parentNode]=rightchild;
								mymap[childNode]=parent;
								vtxmymap[parent]=childNode;
								vtxmymap[rightchild]=parentNode;
								parent=rightchild;
							}
							else end=true;
						}
					}
				}
			}
		}
	}
	
	void update(int child) {
		if(update[child]==updatevalue) return;
		boolean end=false;
		while(!end) {
			update[child]=updatevalue;
			int parent=child/2;
			if(parent<1) end=true;
			else {
				if(mylist[parent]>mylist[child]) {
					int parentNode=vtxmymap[parent];
					int childNode=vtxmymap[child];
					int parentDeg=mylist[parent];
					int childDeg=mylist[child];
					mylist[parent]=childDeg;
					mylist[child]=parentDeg;
					mymap[parentNode]=child;
					mymap[childNode]=parent;
					vtxmymap[parent]=childNode;
					vtxmymap[child]=parentNode;
					parent=child;
				}
				else end=true;
			}
		}
	}
	
	int peek() {
		return mylist[1];
	}
	
	int pop() {
		int toreturn=mylist[1];
		removed[vtxmymap[1]]=1;
		mylist[1]=mylist[size];
		int changedNode=vtxmymap[size];
		vtxmymap[1]=changedNode;
		mymap[changedNode]=1;
		boolean end=false;
		size--;
		if(size==0) end=true;
		int parent=1;
		while(!end) {
			int leftchild=2*parent;
			int rightchild=2*parent+1;
			if(leftchild>size) {
				end=true;
			}
			else if(rightchild>size) {
				if(mylist[leftchild]<mylist[parent]) {
					int parentNode=vtxmymap[parent];
					int childNode=vtxmymap[leftchild];
					int parentDeg=mylist[parent];
					int childDeg=mylist[leftchild];
					mylist[parent]=childDeg;
					mylist[leftchild]=parentDeg;
					mymap[parentNode]=leftchild;
					mymap[childNode]=parent;
					vtxmymap[parent]=childNode;
					vtxmymap[leftchild]=parentNode;
					parent=leftchild;
				}
				else end=true;
			}
			else {
				if(mylist[leftchild]<=mylist[rightchild]) {
					if(mylist[leftchild]<mylist[parent]) {
						int parentNode=vtxmymap[parent];
						int childNode=vtxmymap[leftchild];
						int parentDeg=mylist[parent];
						int childDeg=mylist[leftchild];
						mylist[parent]=childDeg;
						mylist[leftchild]=parentDeg;
						mymap[parentNode]=leftchild;
						mymap[childNode]=parent;
						vtxmymap[parent]=childNode;
						vtxmymap[leftchild]=parentNode;
						parent=leftchild;
					}
					else end=true;
				}
				else {
					if(mylist[rightchild]<mylist[parent]) {
						int parentNode=vtxmymap[parent];
						int childNode=vtxmymap[rightchild];
						int parentDeg=mylist[parent];
						int childDeg=mylist[rightchild];
						mylist[parent]=childDeg;
						mylist[rightchild]=parentDeg;
						mymap[parentNode]=rightchild;
						mymap[childNode]=parent;
						vtxmymap[parent]=childNode;
						vtxmymap[rightchild]=parentNode;
						parent=rightchild;
					}
					else end=true;
				}
			}
		}
		
		
		return toreturn;
	}
	
}


 
 class DisJoint {
		int[] parent;
		int[] rank;
		int[] size;
		DisJoint(int n){
			
			parent=new int[n+1];
			rank=new int[n+1];
			for(int i=0;i<=n;i++) {
				parent[i]=i;
			}
		}

		int find(int value) {
			int par=parent[value];
			if(par==value)
				return par;
			parent[value]=find(par);
			return parent[value];
		}
		
		void union(int data1,int data2) {
			int parent1=find(data1);
			int parent2=find(data2);
			if(parent1!=parent2) {
				if(rank[parent1]>=rank[parent2]) {
					parent[parent2]=parent1;
					if(rank[parent1]==rank[parent2])
						rank[parent1]++;
				}
				else {
					parent[parent1]=parent2;	
		}

		}
		}
}

 
 class Reader {
	    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 nextLine() throws IOException{
	    	return reader.readLine();
	    }
	    static String next() throws IOException {
	        while ( ! tokenizer.hasMoreTokens() ) {
	            //TODO add check for eof if necessary
	            tokenizer = new StringTokenizer(
	                   reader.readLine() );
	        }
	        return tokenizer.nextToken();
	    }
	    
	    static int nextInt() throws IOException {
	        return Integer.parseInt( next() );
	    }
	    static long nextLong() throws IOException {
	        return Long.parseLong( next() );
	    }
	    static double nextDouble() throws IOException {
	        return Double.parseDouble( next() );
	    }
	}

