Problem: Consider the following experiment. You have a deck of m cards, and exactly one card is a joker. n times, you do the following: shuffle the deck, take the top card of the deck, look at it and return it into the deck.

Let x be the number of times you have taken the joker out of the deck during this experiment. Assuming that every time you shuffle the deck, all m! possible permutations of cards are equiprobable, what is the expected value of x^k? Print the answer modulo 998244353.

Input

The only line contains three integers n, m and k (1 ≤ n, m < 998244353, 1 ≤ k ≤ 5000).

Output

Print one integer — the expected value of x^k, taken modulo 998244353 (the answer can always be represented as an irreducible fraction a/b, where b mod 998244353 ≠ 0; you have to print a ⋅ b^{-1} mod 998244353).

Examples

Input


1 1 1


Output


1


Input


1 1 5000


Output


1


Input


2 2 2


Output


499122178


Input


998244352 1337 5000


Output


326459680

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author ijxjdjd
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        Cards solver = new Cards();
        solver.solve(1, in, out);
        out.close();
    }

    static class Cards {
        long MOD = 998244353;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            long N = in.nextInt();
            long M = in.nextInt();
            int K = in.nextInt();
            long mod = MathUtils.modFraction(1, M, MOD);
            long[] expect = new long[K + 1];
            expect[0] = 1;
            long[] poly = new long[K + 1];
            poly[0] = 1;
            long curExpect = 1;
            for (int k = 1; k <= K; k++) {
                curExpect *= (N - (k - 1));
                curExpect %= MOD;
                curExpect *= mod;
                curExpect %= MOD;
                for (int i = k; i >= 0; i--) {
                    poly[i] = (i > 0 ? poly[i - 1] : 0) + (-(k - 1)) * poly[i];
                    poly[i] = MathUtils.mod(poly[i], MOD);
                }
                expect[k] = curExpect;
                for (int i = k - 1; i >= 0; i--) {
                    expect[k] -= poly[i] * expect[i];
                    expect[k] = MathUtils.mod(expect[k], MOD);
                }
            }
            out.println(expect[K]);
        }

    }

    static class MathUtils {
        public static long inverse(long a, long mod) {
            long[] inv = extended_gcd(a, mod);
            if (inv[0] != 1) {
                return 0;
            } else {
                return (inv[1] + 2 * mod) % mod;
            }
        }

        public static long modFraction(long a, long b, long mod) {
            //a is numerator, b is denominator
            long invB = inverse(b, mod);
            if (invB == 0) {
                return -1;
            } else {
                return (invB * a) % mod;
            }
        }

        public static long[] extended_gcd(long a, long b) {
            //three numbers, first is gcd, second is x, third is y
            if (a == 0) {
                return new long[]{b, 0, 1};
            }
            long[] next = extended_gcd(b % a, a);
            long tempX = next[1];
            next[1] = next[2] - (b / a) * next[1];
            next[2] = tempX;
            return next;
        }

        public static long mod(long a, long mod) {
            return (a + (Math.abs(a) + mod - 1) / mod * mod) % mod;
        }

    }

    static class InputReader {
        public BufferedReader reader;
        public StringTokenizer tokenizer;

        public InputReader(InputStream stream) {
            reader = new BufferedReader(new InputStreamReader(stream), 32768);
            tokenizer = null;
        }

        public String next() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

    }
}