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.*;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;
/* 
																yash jobanputra
																	DA-IICT
*/
public class yash {
	private static InputStream stream;
	private static byte[] buf = new byte[1024];
	private static int curChar;
	private static int numChars;
	private static SpaceCharFilter filter;
	private static PrintWriter pw;
	private static long mod = 1000000000 + 7;
	private static long mod1 = 1000000000 + 9;
	private static int MAX=1000001;
	private static int block;
	private static int[] cost;
	private static int times1;
	private static int times2;
	private static boolean[] vis;
	private static int[] mark;
	private static boolean ff;
	private static void soln(){
		int n=ni();
		int m=ni();int k=ni();
		if(k==0)
			pw.println(m);
		else
		{
			long mod=998244353;
			long fn=f(n-1,mod);
			long fk=f(k,mod);
			long fnk=f(n-1-k,mod);
			long fki=mmi(fk,mod);
			long fnki=mmi(fnk,mod);
			long t1=(((fn*fki)%mod)*fnki)%mod;
			long ans=(((t1*m)%mod)*pow(m-1,k,mod))%mod;
			pw.println(ans);
		}
		
	}
	public static long f(long number,long m) {
	      if (number <= 1) return 1;
	      else return (number * f(number - 1,m))%m;
	   }
	public static long mmi(long a, long m) 
	{ 
	    long m0 = m; 
	    long y = 0, x = 1; 
	  
	    if (m == 1) 
	      return 0; 
	  
	    while (a > 1) 
	    { 
	        // q is quotient 
	        long q = a / m; 
	        long t = m; 
	  
	        // m is remainder now, process same as 
	        // Euclid's algo 
	        m = a % m; a = t; 
	        t = y; 
	  
	        // Update y and x 
	        y = x - q * y; 
	        x = t; 
	    } 
	  
	    // Make x positive 
	    if (x < 0) 
	       x += m0; 
	  
	    return x; 
	} 
	public static class segtree{ 
		static int[] tree=new int[10000000];
		static int[] lazy=new int[10000000];
		public static void initial()
		{
			Arrays.fill(lazy, 0);
		}
		public static void build(int[] arr,int node,int l,int r)
		{
			if(l==r)
			{
				tree[node]=arr[l];
			}
			else
			{
				int m=(l+r)/2;
				build(arr,(2*node)+1,l,m);
				build(arr,(2*node)+2,m+1,r);
				tree[node]=tree[2*node+1]+tree[(2*node)+2];
			}
		}
		public static void updater(int[] arr,int node,int l,int r,int s,int e,int val)
		{
			if(lazy[node]!=0)
			{
				tree[node]+=(r-l+1)*lazy[node];
				if(l!=r)
				{
					lazy[2*node+1]+=lazy[node];
					lazy[2*node+2]+=lazy[node];
				}
				lazy[node]=0;
			}
			if(s<=l && e>=r)
			{
				tree[node]+=(r-l+1)*val;
				if(l!=r)
				{
					lazy[2*node+1]+=val;
					lazy[2*node+2]+=val;
				}
			}
			else if(!(e<l || r<s))
			{
				int m=(l+r)/2;
				updater(arr,2*node+1,l,m,s,e,val);
				updater(arr,2*node+2,m+1,r,s,e,val);
				tree[node]=tree[2*node+1]+tree[2*node+2];
			}
		}
		public static void update(int[] arr,int node,int l,int r,int ind,int val)
		{
			if(l==r)
			{
				arr[ind]+=val;
				tree[node]+=val;
			}
			else
			{
				int m=(l+r)/2;
				if(l<=ind && ind<=m)
				{
					update(arr,(2*node+1),l,m,ind,val);
				}
				else
				{
					update(arr,(2*node+2),m+1,r,ind,val);
				}
				tree[node]=tree[2*node+1]+tree[2*node+2];
			}
		}
		public static int query(int node,int l,int r,int s,int e)
		{
			if(lazy[node]!=0)
			{
				tree[node]+=(r-l+1)*lazy[node];
				if(l!=r)
				{
					lazy[2*node+1]+=lazy[node];
					lazy[2*node+2]+=lazy[node];
				}
				lazy[node]=0;
			}
			if(e<l || r<s)
				return 0;
			if(s<=l && e>=r)
				return tree[node];
			int m=(l+r)/2;
			int p1=query((2*node+1),l,m,s,e);
			int p2=query((2*node+2),m+1,r,s,e);
			return (p1+p2);
		}
	}
	
	public static void dfs(ArrayList<Integer>[] gr,int v)
	{
		//pw.println(mark[v]+" kk");
		vis[v]=true;
		ArrayList<Integer> arr=gr[v];
		for(int i=0;i<arr.size();i++)
		{
			if(!vis[arr.get(i)])
			{
				if(mark[v]==1)
					{mark[arr.get(i)]=2;times2++;}
				else
					{mark[arr.get(i)]=1;times1++;}
				dfs(gr,arr.get(i));
			}
			else if(mark[arr.get(i)]==mark[v])
				{ff=false;}
		}
		
	}
	private static class Pair implements Comparable<Pair>{
		int v,i,k;Pair j;
		public Pair(int a,int b){
			v=a;
			i=b;
		}
		@Override
		public int compareTo(Pair arg0) {
			{
				return this.v-arg0.v;
			}
		}
	}
	private static long pow(long a, long b, long c) {
		if (b == 0)
			return 1;
		long p = pow(a, b / 2, c);
		p = (p * p) % c;
		return (b % 2 == 0) ? p : (a * p) % c;
	}
	private static long gcd(long n, long l) {
		if (l == 0)
			return n;
		return gcd(l, n % l);
	}
	private static int gcd(int n, int l) {
		if (l == 0)
			return n;
		return gcd(l, n % l);
	}
	private static long max(long a, long b) {
		if (a > b)
			return a;
		return b;
	}

	private static long min(long a, long b) {
		if (a < b)
			return a;
		return b;
	}

	public static void main(String[] args) throws Exception {
		new Thread(null,new Runnable(){
			@Override
			public void run() {
				/*try {
					InputReader(new FileInputStream("C:\\Users\\hardik\\Desktop\\C-small-1-attempt1.in"));
				} catch (FileNotFoundException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}*/
				InputReader(System.in);
				pw = new PrintWriter(System.out);
				/*try {
					pw=new PrintWriter(new FileOutputStream("C:\\Users\\hardik\\Desktop\\out.txt"));
				} catch (FileNotFoundException e) {
					// TODO Auto-generated catch block
					e.printStackTrace();
				}*/
				soln();
				pw.close();
			}
		},"1",1<<26).start();
	}

	public static void InputReader(InputStream stream1) {
		stream = stream1;
	}

	private static boolean isWhitespace(int c) {
		return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
	}

	private static boolean isEndOfLine(int c) {
		return c == '\n' || c == '\r' || c == -1;
	}

	private static int read() {
		if (numChars == -1)
			throw new InputMismatchException();
		if (curChar >= numChars) {
			curChar = 0;
			try {
				numChars = stream.read(buf);
			} catch (IOException e) {
				throw new InputMismatchException();
			}
			if (numChars <= 0)
				return -1;
		}
		return buf[curChar++];
	}

	private static int ni() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		int res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}

	private static long nl() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		int sgn = 1;
		if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
				throw new InputMismatchException();
			res *= 10;
			res += c - '0';
			c = read();
		} while (!isSpaceChar(c));
		return res * sgn;
	}
	private static double nd()
    {
        double ret = 0, div = 1;
        int c = read();
        while (c <= ' ')
            c = read();
        boolean neg = (c == '-');
        if (neg)
            c = read();

        do {
            ret = ret * 10 + c - '0';
        }
        while ((c = read()) >= '0' && c <= '9');

        if (c == '.')
        {
            while ((c = read()) >= '0' && c <= '9')
            {
                ret += (c - '0') / (div *= 10);
            }
        }

        if (neg)
            return -ret;
        return ret;
    }
	private static String nextToken() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isSpaceChar(c));
		return res.toString();
	}

	private static String nli() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		StringBuilder res = new StringBuilder();
		do {
			res.appendCodePoint(c);
			c = read();
		} while (!isEndOfLine(c));
		return res.toString();
	}
	
	private static int[] nia(int n) {
		int[] arr = new int[n];
		for (int i = 0; i < n; i++) {
			arr[i] = ni();
		}
		return arr;
	}

	private static long[] nla(int n) {
		long[] arr = new long[n];
		for (int i = 0; i < n; i++) {
			arr[i] = nl();
		}
		return arr;
	}

	private static void pa(int[] arr) {
		for (int i = 0; i < arr.length; i++) {
			pw.print(arr[i] + " ");
		}
		pw.println();
		return;
	}

	private static void pa(long[] arr) {
		for (int i = 0; i < arr.length; i++) {
			pw.print(arr[i] + " ");
		}
		pw.println();
		return;
	}

	private static boolean isSpaceChar(int c) {
		if (filter != null)
			return filter.isSpaceChar(c);
		return isWhitespace(c);
	}
	private static char nc() {
		int c = read();
		while (isSpaceChar(c))
			c = read();
		char c1=(char)c;
		while(!isSpaceChar(c))
			c=read();
		return c1;
	}
	public String ns() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        StringBuilder res = new StringBuilder();
        do {
            res.appendCodePoint(c);
            c = read();
        } while (!isSpaceChar(c));
        return res.toString();
    }
	private interface SpaceCharFilter {
		public boolean isSpaceChar(int ch);
	}
}