Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
D. Vasily the Bear and Beautiful Strings

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputVasily the Bear loves beautiful strings. String *s* is beautiful if it meets the following criteria:

- 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. - 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 (10^{9} + 7).

Input

The first line of the input contains three space-separated integers *n*, *m*, *g* (0 ≤ *n*, *m* ≤ 10^{5}, *n* + *m* ≥ 1, 0 ≤ *g* ≤ 1).

Output

Print a single integer — the answer to the problem modulo 1000000007 (10^{9} + 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.

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Oct/29/2020 08:03:37 (h2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|