Vasily the Bear loves beautiful strings. String s is beautiful if it meets the following criteria: 

  1. String s only consists of characters 0 and 1, at that character 0 must occur in string s exactly n times, and character 1 must occur exactly m times. 
  2. We can obtain character g from string s with some (possibly, zero) number of modifications. The character g equals either zero or one. 



A modification of string with length at least two is the following operation: we replace two last characters from the string by exactly one other character. This character equals one if it replaces two zeros, otherwise it equals zero. For example, one modification transforms string "01010" into string "0100", two modifications transform it to "011". It is forbidden to modify a string with length less than two.

Help the Bear, count the number of beautiful strings. As the number of beautiful strings can be rather large, print the remainder after dividing the number by 1000000007 (109 + 7). 

Input

The first line of the input contains three space-separated integers n, m, g (0 ≤ n, m ≤ 105, n + m ≥ 1, 0 ≤ g ≤ 1).

Output

Print a single integer — the answer to the problem modulo 1000000007 (109 + 7).

Examples

Input

1 1 0


Output

2


Input

2 2 0


Output

4


Input

1 1 1


Output

0

Note

In the first sample the beautiful strings are: "01", "10".

In the second sample the beautiful strings are: "0011", "1001", "1010", "1100".

In the third sample there are no beautiful strings.
import java.io.InputStreamReader;
import java.io.IOException;
import java.io.BufferedReader;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.InputStream;

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

class TaskD {

    private static final int MODULO = 1000000007;
    private static long[] factorial;

    public void solve(int testNumber, InputReader in, PrintWriter out) {
        int n = in.nextInt();
        int m = in.nextInt();
        int g = in.nextInt();
        long answer = 0;
        if (m == 0) {
            if (g + (n & 1) == 1)
                answer++;
        } else {
            calculateFactorials(n + m);
            if (m == 1)
                answer = n / 2 + 1 - (n & 1);
            else {
                for (int i = 1; i <= n; i += 2) {
                    answer += combination(n + m - i - 1, n - i);
                    if (answer > MODULO)
                        answer -= MODULO;
                }
            }
            if (g == 0)
                answer = (combination(n + m, n) - answer);
            answer %= MODULO;
            while (answer < 0)
                answer += MODULO;
        }
        out.println(answer);
    }

    private void calculateFactorials(int until) {
        factorial = new long[until + 1];
        factorial[0] = factorial[1] = 1;
        for (int i = 2; i <= until; i++)
            factorial[i] = i * factorial[i - 1] % MODULO;
    }

    private long combination(int n, int k) {
        return factorial[n] * modInverse(factorial[k] * factorial[n - k] % MODULO) % MODULO;
    }

    private long modInverse(long n) {
        return binaryPow(n, MODULO - 2);
    }

    private long binaryPow(long base, int power) {
        if (power == 0)
            return 1;
        long result = binaryPow(base, power >> 1);
        result = result * result % MODULO;
        if ((power & 1) == 1)
            result = result * base % MODULO;
        return result;
    }
}

class InputReader {

    private static BufferedReader bufferedReader;
    private static StringTokenizer stringTokenizer;

    public InputReader(InputStream inputStream) {
        bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
        stringTokenizer = null;
    }

    public String next() {
        while(stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
            try {
                stringTokenizer = new StringTokenizer(bufferedReader.readLine());
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return stringTokenizer.nextToken();
    }

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

    }

