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.InputMismatchException;
import java.io.IOException;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Sparsh Sanchorawala
 */
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);
        FCards solver = new FCards();
        solver.solve(1, in, out);
        out.close();
    }

    static class FCards {
        long mod = 998244353;

        long modExp(long x, long y) {
            if (y == 0)
                return 1;
            if (y == 1)
                return x;
            long ret = modExp(x, y >> 1);
            ret = ret * ret % mod;
            if ((y & 1) == 1)
                ret = ret * x % mod;
            return ret;
        }

        public void solve(int testNumber, InputReader s, PrintWriter w) {
            int n = s.nextInt(), m = s.nextInt(), k = s.nextInt();
            //dp[tuple size][number of distinct elements] = number of such tuples
            long[][] dp = new long[k + 1][Math.min(n, k) + 1];
            dp[0][0] = 1;
            for (int i = 1; i <= k; i++) {
                for (int j = 1; j <= Math.min(n, k); j++) {
                    dp[i][j] = (dp[i][j] + dp[i - 1][j] * j % mod) % mod;
                    dp[i][j] = (dp[i][j] + dp[i - 1][j - 1] * (n - j + 1) % mod) % mod;
                }
            }
            long invm = modExp(m, mod - 2);
            long res = 0;
            long prob = 1;
            for (int i = 0; i <= Math.min(n, k); i++) {
                res = (res + dp[k][i] * prob % mod) % mod;
                prob = prob * invm % mod;
            }
            w.println(res);
        }

    }

    static class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;
        private InputReader.SpaceCharFilter filter;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public 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++];
        }

        public int nextInt() {
            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;
        }

        public boolean isSpaceChar(int c) {
            if (filter != null) {
                return filter.isSpaceChar(c);
            }
            return isWhitespace(c);
        }

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

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);

        }

    }
}