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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collection;
import java.util.List;

public class D {
    
    public static void main(final String[] args) throws IOException {
        try (
                final BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
                final PrintWriter out = new PrintWriter(System.out)
                ) {
            String line;
            for(line = in.readLine(); line != null && !line.isEmpty(); line = in.readLine()) {
                final String[] parts = line.split(" ");
                if(parts.length != 3) {
                    throw new IOException();
                }
                final int numberZeros = Integer.parseInt(parts[0]);
                final int numberOnes = Integer.parseInt(parts[1]);
                final int resultCipher = Integer.parseInt(parts[2]);
                solve(numberZeros, numberOnes, resultCipher, out);
                out.flush();
            }
        }
    }
    
    private static void solve(final int numberZeros, final int numberOnes, final int resultCipher, final PrintWriter out) {
        ModNumber result = new ModNumber(0);
        final boolean degenerateSatisfy = (numberZeros & 1) != resultCipher;
        //System.out.println(degenerateSatisfy);
        if(numberOnes == 0) {
            result = new ModNumber(!degenerateSatisfy ? 0 : 1);
        } else {
            final List<Integer> inv = new ArrayList<>(numberZeros + 1);
            if(numberOnes == 1 && degenerateSatisfy) {
                result = new ModNumber(1);
            }
            ModNumber combination = new ModNumber(degenerateSatisfy ? numberOnes : 1);
            for(int i = !degenerateSatisfy ? 0 : 1; i <= numberZeros; i += 2) {
                if(i > 1) {
                    combination = combination.multiply(
                            new ModNumber(numberOnes + i - 2)).multiply(
                            new ModNumber(numberOnes + i - 1)).multiply(
                            ModNumber.inverse(i - 1, inv)).multiply(
                            ModNumber.inverse(i, inv));
                }
                //System.out.println((long)ModNumber.mod / 2 * (ModNumber.mod - 1) % ModNumber.mod);
                //System.out.println(ModNumber.inverse(2, inv));
                //System.out.println(ModNumber.inverse(2, inv).multiply(new ModNumber(2)));
                if(i == 0 && numberOnes == 1) {
                    continue;
                }
                result = result.add(combination);
            }
        }
        out.println(result);
    }
    
    private static class ModNumber {
        public static final int mod = 1000000007; //10^9 + 7
        private final int number;
        
        public ModNumber(final int number) {
            this.number = number;
        }
        
        public static ModNumber inverse(final int number, final List<Integer> inv) {
            CollectionUtils.increaseToSize(inv, number + 1);
            if(inv.get(number) == null) {
                inv.set(number, number == 1 ? 1 : (int)((mod / number * (long)(mod - inverse(mod % number, inv).number)) % mod));
            }
            return new ModNumber(inv.get(number));
        }
        
        public ModNumber add(final ModNumber n) {
            int result = number + n.number;
            if(result >= mod) {
                result -= mod;
            }
            return new ModNumber(result);
        }
        
        public ModNumber multiply(final ModNumber n) {
            return new ModNumber((int)((long)number * n.number % mod));
        }
        
        @Override
        public String toString() {
            return number + "";
        }
    }
    
    private static class CollectionUtils {
        
        public static void increaseToSize(Collection<?> collection, final int size) {
            while(collection.size() < size) {
                collection.add(null);
            }
        }
    }
    
}
