// package other2019.keyence2019;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {
    static long __startTime = System.currentTimeMillis();

    static final long MOD = 1000000007;

    public static void main(String[] args) {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);


        int n = in.nextInt();
        int m = in.nextInt();
        int[] a = new int[n];
        int[] b = new int[m];
        for (int i = 0; i < n ; i++) {
            a[i] = in.nextInt();
        }
        for (int i = 0; i < m ; i++) {
            b[i] = in.nextInt();
        }
        Arrays.sort(a);
        Arrays.sort(b);

        int ai = n-1;
        int bi = m-1;
        long ways = 1;

        long free = 0;
        int seek = n*m+1;
        while (seek >= 2) {
            seek--;
            // debug(seek, ways, free);
            boolean row = false;
            boolean col = false;
            if (ai >= 0 && a[ai] == seek) {
                row = true;
            }
            if (bi >= 0 && b[bi] == seek) {
                col = true;
            }
            if (!row && !col) {
                ways *= free;
                ways %= MOD;
                if (free == 0) {
                    break;
                }
                free -= 1;
                continue;
            }
            if (row && col) {
                free += n-ai-1;
                free += m-bi-1;
                ai--;
                bi--;
                continue;
            }
            if (row) {
                long way = m-bi-1;
                ways *= way;
                free += way-1;
                ways %= MOD;
                ai--;
                continue;
            }
            if (col) {
                long way = n-ai-1;
                ways *= way;
                free += way-1;
                ways %= MOD;
                bi--;
                continue;
            }

        }

        out.println(ways % MOD);
        out.flush();
    }

    private static void printTime(String label) {
        debug(label, System.currentTimeMillis() - __startTime);
    }

    private static void debug(Object... o) {
        System.err.println(Arrays.deepToString(o));
    }

    public static class InputReader {
        private static final int BUFFER_LENGTH = 1 << 12;
        private InputStream stream;
        private byte[] buf = new byte[BUFFER_LENGTH];
        private int curChar;
        private int numChars;

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

        private int next() {
            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 char nextChar() {
            return (char) skipWhileSpace();
        }

        public String nextToken() {
            int c = skipWhileSpace();
            StringBuilder res = new StringBuilder();
            do {
                res.append((char) c);
                c = next();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public int nextInt() {
            return (int) nextLong();
        }

        public long nextLong() {
            int c = skipWhileSpace();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') {
                    throw new InputMismatchException();
                }
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public double nextDouble() {
            return Double.valueOf(nextToken());
        }

        int skipWhileSpace() {
            int c = next();
            while (isSpaceChar(c)) {
                c = next();
            }
            return c;
        }

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

Measured memory_bytes: 23124