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  1. Prepare
  2. Mathematics
  3. Combinatorics
  4. Parity Party

Parity Party

We need your help to divide candies at a very unusual party!
There are different candies in total. There are three kinds of people at party:

  • of them want to get odd number of candies,
  • of them want to get even number of candies,
  • simply don't care about parity of candies they get.

Find out the number of ways to divide all of candies between everybody ( people), such that everyone is satisfied. Some people may not receive a candy.

Input Format

One line of input contains four space-separated integers .

Constraints

  • ,
  • ,
  • .

Output Format

Print one line containing answer to the problem modulo .

Sample Input 0

3 1 1 0

Sample Output 0

4

Explanation 0

Let be three different candies. One of the visitors wants to get odd number of candies, the other wants to get even number. There are four good splittings:
.