Problem: After a terrifying forest fire in Berland a forest rebirth program was carried out. Due to it N rows with M trees each were planted and the rows were so neat that one could map it on a system of coordinates so that the j-th tree in the i-th row would have the coordinates of (i, j). However a terrible thing happened and the young forest caught fire. Now we must find the coordinates of the tree that will catch fire last to plan evacuation.

The burning began in K points simultaneously, which means that initially K trees started to burn. Every minute the fire gets from the burning trees to the ones that aren’t burning and that the distance from them to the nearest burning tree equals to 1.

Find the tree that will be the last to start burning. If there are several such trees, output any.

Input

The first input line contains two integers N, M (1 ≤ N, M ≤ 2000) — the size of the forest. The trees were planted in all points of the (x, y) (1 ≤ x ≤ N, 1 ≤ y ≤ M) type, x and y are integers.

The second line contains an integer K (1 ≤ K ≤ 10) — amount of trees, burning in the beginning. 

The third line contains K pairs of integers: x1, y1, x2, y2, ..., xk, yk (1 ≤ xi ≤ N, 1 ≤ yi ≤ M) — coordinates of the points from which the fire started. It is guaranteed that no two points coincide.

Output

Output a line with two space-separated integers x and y — coordinates of the tree that will be the last one to start burning. If there are several such trees, output any.

Examples

Input

3 3
1
2 2


Output

1 1


Input

3 3
1
1 1


Output

3 3


Input

3 3
2
1 1 3 3


Output

2 2

Solution (in JAVA):

Solution:
import java.io.*;
import java.util.*;

public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    
    long MAX = 100000L, MOD = 1000000007L, INF = (long) 1e18;
    
    boolean isValid(int x, int y, int n, int m){
        return x>=0 && y>=0 && x<n && y<m;
    }
    
    void solve(int TC) throws Exception {
        helper hp = new helper(MOD, (int)MAX);
        hp.initIO("input.txt", "output.txt");
        int n = hp.nextInt(), m = hp.nextInt();
        boolean[][] a = new boolean[n][m];
        int k = hp.nextInt();
        ArrayDeque<int[]> q = new ArrayDeque<>();
        for(int i=0;i<k;i++){
            int x = hp.nextInt() - 1;
            int y = hp.nextInt() - 1;
            a[x][y] = true;
            q.add(new int[]{x,y});
        }
        int lastX = 0,lastY = 0;
        int[] dx = new int[]{1,-1,0,0};
        int[] dy = new int[]{0,0,1,-1};
        while(!q.isEmpty()){
            int[] X = q.pollFirst();
            for(int i=0;i<4;i++){
                int x = X[0] + dx[i];
                int y = X[1] + dy[i];
                if(isValid(x,y,n,m) && !a[x][y]){
                    a[x][y] = true;
                    lastX = x;
                    lastY = y;
                    q.add(new int[]{x,y});
                }
            }
        }
        hp.println((lastX+1) + " " + (lastY+1)); hp.flush();
    }
    
    boolean TestCases = false;
    public static void main(String[] args) throws Exception { new Main().run(); }
    
    void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
    static void dbg(Object... o){System.err.println(Arrays.deepToString(o));}
    
    void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        long s = System.currentTimeMillis();
        int T = TestCases ? ni() : 1;
        for(int t=1;t<=T;t++) solve(t);
        out.flush();
        if(!INPUT.isEmpty())tr(System.currentTimeMillis()-s+"ms");
    }
    
    void p(Object o) { out.print(o); }
    void pn(Object o) { out.println(o); }
    void pni(Object o) { out.println(o);out.flush(); }
    double PI = 3.141592653589793238462643383279502884197169399;
    
    int ni() {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-') {
            minus = true;
            b = readByte();
        }
        while(true) {
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    long nl() {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-') {
            minus = true;
            b = readByte();
        }
        while(true) {
            if(b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    double nd() { return Double.parseDouble(ns()); }
    char nc() { return (char)skip(); }
    
    int BUF_SIZE = 1024 * 8;
    byte[] inbuf = new byte[BUF_SIZE];
    int lenbuf = 0, ptrbuf = 0;
    
    int readByte() {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        } return inbuf[ptrbuf++];
    }
    
    boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
    int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    String ns() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))) {
            sb.appendCodePoint(b); b = readByte();
        } return sb.toString();
    }
    
    char[] ns(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        } return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    void tr(Object... o) { if(INPUT.length() > 0)System.out.println(Arrays.deepToString(o)); }
}


class helper {
    final long MOD;
    final int MAXN;
    final Random rnd;

    public helper(long mod, int maxn) {
        MOD = mod;
        MAXN = maxn;
        rnd = new Random();
    }
	
    static final int BUFSIZE = 1 << 20;
    static byte[] buf;
    static int index, total;
    static InputStream in;
    static BufferedWriter bw;


    public void initIO(InputStream is, OutputStream os) {
        try {
            in = is;
            bw = new BufferedWriter(new OutputStreamWriter(os));
            buf = new byte[BUFSIZE];
        } catch (Exception e) {
        }
    }

    public void initIO(String inputFile, String outputFile) {
        try {
            in = new FileInputStream(inputFile);
            bw = new BufferedWriter(new OutputStreamWriter(
                    new FileOutputStream(outputFile)));
            buf = new byte[BUFSIZE];
        } catch (Exception e) {
            e.printStackTrace();
        }
    }
    
    private int scan() throws Exception {
        if (index >= total) {
            index = 0;
            total = in.read(buf);
            if (total <= 0)
                return -1;
        }
        return buf[index++];
    }

    public String next() throws Exception {
        int c;
        for (c = scan(); c <= 32; c = scan()) ;
        StringBuilder sb = new StringBuilder();
        for (; c > 32; c = scan())
            sb.append((char) c);
        return sb.toString();
    }

    public int nextInt() throws Exception {
        int c, val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+')
            c = scan();
        for (; c >= '0' && c <= '9'; c = scan())
            val = (val << 3) + (val << 1) + (c & 15);
        return neg ? -val : val;
    }

    public long nextLong() throws Exception {
        int c;
        long val = 0;
        for (c = scan(); c <= 32; c = scan()) ;
        boolean neg = c == '-';
        if (c == '-' || c == '+')
            c = scan();
        for (; c >= '0' && c <= '9'; c = scan())
            val = (val << 3) + (val << 1) + (c & 15);
        return neg ? -val : val;
    }
    
    public long pow(long base, long exp, long MOD) {
        base %= MOD;
        long ret = 1;
        while (exp > 0) {
            if ((exp & 1) == 1) ret = ret * base % MOD;
            base = base * base % MOD;
            exp >>= 1;
        }
        return ret;
    }
    
    public void println(Object a) throws Exception {
        bw.write(a.toString()+"\n");
    }
    public void print(Object a) throws Exception {
        bw.write(a.toString());
    }
    public void flush() throws Exception {
        bw.flush();
    }
    
    public static int[] sieve;
    public static ArrayList<Integer> primes;
    
    public void setSieve() {
        primes = new ArrayList<>();
        sieve = new int[MAXN];
        int i, j;
        for (i = 2; i < MAXN; ++i)
            if (sieve[i] == 0) {
                primes.add(i);
                for (j = i; j < MAXN; j += i) {
                    sieve[j] = i;
                }
            }
    }
}