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:
//package com.company;

import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    public static class Task {
        int mod = 998244353;
        int add(int a, int b) {
            int c = a + b;
            if (c >= mod) return c - mod;
            if (c < 0) return  c+ mod;
            return c;
        }
        int mult(int a, int b) {
            return (int) ((long) a * b % mod);
        }
        int mult(int... x) {
            int r = 1;
            for (int y: x) {
                r = mult(r, y);
            }
            return r;
        }
        int[][] stirling;
        void pre() {
            stirling = new int[5001][5001];
            for (int i = 0; i < stirling.length; i++) {
                stirling[i][0] = stirling[0][1] = 0;
            }
            for (int i = 0; i < stirling.length; i++) {
                stirling[i][i] = 1;
            }
            for (int i = 2; i < stirling.length; i++) {
                for (int j = 1; j < i; j++) {
                    stirling[i][j] = add(mult(stirling[i - 1][j], i - 1), stirling[i - 1][j - 1]);
                }
            }
//            System.err.println(Arrays.toString(Arrays.copyOf(stirling[0], 4)));
//            System.err.println(Arrays.toString(Arrays.copyOf(stirling[1], 4)));
//            System.err.println(Arrays.toString(Arrays.copyOf(stirling[2], 4)));
//            System.err.println(Arrays.toString(Arrays.copyOf(stirling[3], 4)));
        }


        public void solve(Scanner sc, PrintWriter pw) throws IOException {
            pre();
            int n = sc.nextInt();
            int m = sc.nextInt();
            int k = sc.nextInt();
            int invm = (int)BigInteger.valueOf(m).modInverse(BigInteger.valueOf(mod)).longValue(); //inv(m);
            int[] pVal = new int[5001];
            pVal[0] = 1;
            int md = n;
            int prp = 1;
            for (int i = 1; i <= k; i++) {
                prp = mult(prp, md, invm);
                md = add(md, -1);
                int sub = prp;
                for (int j = i - 1; j >= 1; j--) {
                    sub = add(sub, mult(stirling[i][j], ((i - j) % 2 == 1) ? pVal[j]: add(0, -pVal[j])));
                }
                pVal[i] = sub;
            }
            pw.println(pVal[k]);
        }

    }

    static long TIME_START, TIME_END;

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
//        Scanner sc = new Scanner(new FileInputStream("input_line"));
        PrintWriter pw = new PrintWriter(new BufferedOutputStream(System.out));
//        PrintWriter pw = new PrintWriter(new FileOutputStream("input_line"));

        Runtime runtime = Runtime.getRuntime();
        long usedMemoryBefore = runtime.totalMemory() - runtime.freeMemory();
        TIME_START = System.currentTimeMillis();
        Task t = new Task();
        t.solve(sc, pw);
        TIME_END = System.currentTimeMillis();
        long usedMemoryAfter = runtime.totalMemory() - runtime.freeMemory();
        pw.close();
        System.err.println("Memory increased: " + (usedMemoryAfter - usedMemoryBefore) / 1000000);
        System.err.println("Time used: " + (TIME_END - TIME_START) + ".");
    }

    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public Scanner(FileReader s) throws FileNotFoundException {
            br = new BufferedReader(s);
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

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

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public boolean ready() throws IOException {
            return br.ready();
        }
    }
}