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.BufferedReader;
import java.io.BufferedWriter;
import java.io.FileReader;
import java.io.FileWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.StringTokenizer;
import java.util.TreeSet;
/*
 * Java Input / Output Class using Buffered/ Input Straem
 * Created by @neelbhallabos
 * File Created at: Mar 25, 2019
 */
public class BrickEnumeration {
	public static BufferedReader sc = new BufferedReader(new InputStreamReader(System.in));
	public static StringTokenizer st;
	public static PrintWriter pw = new PrintWriter(System.out);
	final static boolean debugmode = true;
	public static int k = 7; // for 10^9 + k mods.
	public static long STMOD = 1000000000 + k; // 10^9 + k

	public static void main(String[] args) throws IOException {
		int nbricks = getInt();
		int paintbuckets = getInt();
		int numtransitions = getInt();
		long[][] dp = new long[nbricks][numtransitions + 1];
		dp[0][0] = paintbuckets; // the first brick will have 0 transitions
		for(int cbrick = 1; cbrick < nbricks;cbrick++) {
			// handle the no transition case prior.
			dp[cbrick][0] = dp[cbrick-1][0];
			for(int ctransition = 1; ctransition <numtransitions + 1;ctransition++) {
				
					dp[cbrick][ctransition] = dp[cbrick-1][ctransition];
					dp[cbrick][ctransition] %= 998244353;
					dp[cbrick][ctransition] += dp[cbrick-1][ctransition -1] * (paintbuckets-1);
					dp[cbrick][ctransition] %= 998244353;
					
				
			}
		}
		
		submit(dp[dp.length-1][numtransitions],true);
	}
	public static int nchoosekmod(int n, int k, int mod) {
		//(n!)/ (n-k)! k!
		int 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 (int i = 0; i < k; ++i) 
        { 
        res *= (n - i); 
        res /= (i + 1); 
        res %= mod;
        
        } 
      
        return res; 
		
	}
	public static void setInputFile(String fn) throws IOException {
		sc = new BufferedReader(new FileReader(fn));
	}

	public static void setOutputFile(String fn) throws IOException {
		pw = new PrintWriter(new BufferedWriter(new FileWriter(fn)));
	}

	public static int GCD(int a, int b) {
		if (b == 0)
			return a;
		return GCD(b, a % b);
	}

	public static double log(int k, int v) {
		return Math.log(k) / Math.log(v);
	}

	public static long longpower(int a, int b) {
		long[] vals = new long[(int) (log(b, 2) + 2)];
		vals[0] = a;
		vals[1] = a * a;
		for (int i = 1; i < vals.length; i++) {
			vals[i] = vals[i - 1] * vals[i - 1];
		}
		long ans = 1;
		int cindex = 0;
		while (b != 0) {
			if (b % 2 == 1) {
				ans *= vals[cindex];
			}
			cindex += 1;
			b /= 2;
		}
		return ans;

	}

	public static void debug(String toPrint) {
		if (!debugmode) {
			return;
		}
		pw.println("[DEBUG]: " + toPrint);
	}

	public static void submit(int[] k, boolean close) {
		pw.println(Arrays.toString(k));
		if (close) {
			pw.close();
		}
	}

	public static void submit(int p, boolean close) {
		pw.println(Integer.toString(p));
		if (close) {
			pw.close();
		}
	}

	public static void submit(String k, boolean close) {
		pw.println(k);
		if (close) {
			pw.close();
		}
	}

	public static void submit(double u, boolean close) {
		pw.println(Double.toString(u));
		if (close) {
			pw.close();
		}
	}

	public static void submit(long lng, boolean close) {
		pw.println(Long.toString(lng));
		if (close) {
			pw.close();
		}

	}

	public static void submit() {
		pw.close();
	}

	public static int getInt() throws IOException {
		if (st != null && st.hasMoreTokens()) {
			return Integer.parseInt(st.nextToken());
		}
		st = new StringTokenizer(sc.readLine());
		return Integer.parseInt(st.nextToken());
	}

	public static long getLong() throws IOException {
		if (st != null && st.hasMoreTokens()) {
			return Long.parseLong(st.nextToken());
		}
		st = new StringTokenizer(sc.readLine());
		return Long.parseLong(st.nextToken());
	}

	public static double getDouble() throws IOException {
		if (st != null && st.hasMoreTokens()) {
			return Double.parseDouble(st.nextToken());
		}
		st = new StringTokenizer(sc.readLine());
		return Double.parseDouble(st.nextToken());
	}

	public static String getString() throws IOException {
		if (st != null && st.hasMoreTokens()) {
			return st.nextToken();
		}
		st = new StringTokenizer(sc.readLine());
		return st.nextToken();
	}

	public static String getLine() throws IOException {
		return sc.readLine();
	}

	public static int[][] readMatrix(int lines, int cols) throws IOException {
		int[][] matrr = new int[lines][cols];
		for (int i = 0; i < lines; i++) {
			for (int j = 0; j < cols; j++) {
				matrr[i][j] = getInt();
			}
		}
		return matrr;
	}

	public static int[] readArray(int lines) throws IOException {
		int[] ar = new int[lines];
		for (int i = 0; i < lines; i++)
			ar[i] = getInt();
		return ar;
	}

}
/*

public class BrickEnumeration {

}

*/