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.*;

public class Main {
	static int mod = 998244353;
  static int size = 200000;
	static long[] fac = new long[size];
	static long[] finv = new long[size];
	static long[] inv = new long[size];
	static int INF = Integer.MAX_VALUE;

 	public static void main(String[] args){
		Scanner scanner = new Scanner(System.in);
		int n = scanner.nextInt();
		int m = scanner.nextInt();
		int k = scanner.nextInt();

		//dp[i][j]:=i番目のブリキまでの塗り方で、j箇所の隣り合う色が異なる場合の数
		long[][] dp = new long[n+1][n+1];
		dp[1][0] = m;
		for(int i = 1; i < n; i++){
			for(int j = 0; j < i; j++){
				dp[i+1][j] += dp[i][j];
				dp[i+1][j] %= mod;
				dp[i+1][j+1] += dp[i][j]*(m-1);
				dp[i+1][j+1] %= mod;
			}
		}
		System.out.println(dp[n][k]);
	}
	public static boolean isPrime(int n){
		if(n == 1) return false;
		if(n == 2 || n == 3) return true;
		for(int i = 2; i <= Math.sqrt(n); i++){
			if(n % i == 0) return false;
		}
		return true;
	}
	// tar の方が数字が大きいかどうか
	static boolean compare(String tar, String src) {
		if (src == null) return true;
		if (src.length() == tar.length()) {
			int len = tar.length();
			for (int i = 0; i < len; i++) {
				if (src.charAt(i) > tar.charAt(i)) {
					return false;
				} else if (src.charAt(i) < tar.charAt(i)) {
					return true;
				}
			}
			return tar.compareTo(src) > 0 ? true : false;
		} else if (src.length() < tar.length()) {
			return true;
		} else if (src.length() > tar.length()) {
			return false;
		}
		return false;
	}
	public static class Edge{
		int to;
		Edge(int to){
			this.to = to;
		}
	}
	public static void swap(long a, long b){
		long tmp = 0;
		if(a > b){
			tmp = a;
			a = b;
			b = tmp;
		}
	}
  static class Pair implements Comparable<Pair>{
    int first, second;
    Pair(int a, int b){
        first = a;
        second = b;
    }
    @Override
    public boolean equals(Object o){
        if (this == o) return true;
        if (!(o instanceof Pair)) return false;
        Pair p = (Pair) o;
        return first == p.first && second == p.second;
    }
    @Override
    public int compareTo(Pair p){
        return first == p.first ? second - p.second : first - p.first; //firstで昇順にソート
        //return (first == p.first ? second - p.second : first - p.first) * -1; //firstで降順にソート
        //return second == p.second ? first - p.first : second - p.second;//secondで昇順にソート
        //return (second == p.second ? first - p.first : second - p.second)*-1;//secondで降順にソート
    }
  }

  //繰り返し二乗法
  public static long pow(long x, long n){
    long ans = 1;
    while(n > 0){
      if((n & 1) == 1){
        ans = ans * x;
        ans %= mod;
      }
      x = x * x % mod;
      n >>= 1;
    }
    return ans;
  }

	public static long div(long x, long y){
		return (x*pow(y, mod-2))%mod;
	}

  //fac, inv, finvテーブルの初期化、これ使う場合はinitComb()で初期化必要
	public static  void initComb(){
		fac[0] = finv[0] = inv[0] = fac[1] = finv[1] = inv[1] = 1;
		for (int i = 2; i < size; ++i) {
			fac[i] = fac[i - 1] * i % mod;
			inv[i] = mod - (mod / i) * inv[(int) (mod % i)] % mod;
			finv[i] = finv[i - 1] * inv[i] % mod;
		}
	}

	//nCk % mod
	public static long comb(int n, int k){
		return fac[n] * finv[k] % mod * finv[n - k] % mod;
	}

	//n! % mod
	public static long fact(int n){
		return fac[n];
	}

	//(n!)^-1 with % mod
	public static long finv(int n){
		return finv[n];
	}

  static class UnionFind {
    int[] parent;
    public UnionFind(int size) {
      parent = new int[size];
      Arrays.fill(parent, -1);
    }
    public boolean unite(int x, int y) {
      x = root(x);
      y = root(y);
      if (x != y) {
        if (parent[y] < parent[x]) {
          int tmp = y;
          y = x;
          x = tmp;
        }
        parent[x] += parent[y];
        parent[y] = x;
        return true;
      }
      return false;
    }
    public boolean same(int x, int y) {
      return root(x) == root(y);
    }
    public int root(int x) {
      return parent[x] < 0 ? x : (parent[x] = root(parent[x]));
    }
    public int size(int x) {
      return -parent[root(x)];
    }
  }
	public static int upperBound(int[] array, int value) {
			 int low = 0;
			 int high = array.length;
			 int mid;
			 while( low < high ) {
					 mid = ((high - low) >>> 1) + low; // (high + low) / 2
					 if( array[mid] <= value ) {
							 low = mid + 1;
					 } else {
							 high = mid;
					 }
			 }
			 return low;
	 }
	 public static final int lowerBound(final int[] arr, final int value) {
    	int low = 0;
    	int high = arr.length;
    	int mid;
    	while (low < high){
        	mid = ((high - low) >>> 1) + low;    //(low + high) / 2 (オーバーフロー対策)
        	if (arr[mid] < value) {
          	low = mid + 1;
        	} else {
            high = mid;
        	}
    	}
    	return low;
		}
  //n,mの最大公約数
  public static long gcd(long n, long m){
    if(m > n) return gcd(m,n);
    if(m == 0) return n;
    return gcd(m, n%m);
  }
	//3要素のソート
	private class Pair2 implements Comparable<Pair2> {
		String s;
		int p;
		int index;
		public Pair2(String s, int p, int index) {
				this.s = s;
				this.p = p;
				this.index = index;
		}

		public int compareTo(Pair2 other) {
				if (s.equals(other.s)) {
						return other.p - this.p;
				}
				return this.s.compareTo(other.s);
		}
	}
	//c -> intに変換
public static int c2i(char c){
	if('A' <= c && c <= 'Z'){
		return c - 'A';
	}else{
		return c - 'a' + 26;
	}
}
// int -> charに変換
public static char i2c(int i){
	if(0 <= i && i < 26){
			return (char)(i + 'A');
	}else{
			return (char)(i + 'a' - 26);
	}
}

}
