Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-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

A. Lengthening Sticks

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou are given three sticks with positive integer lengths of *a*, *b*, and *c* centimeters. You can increase length of some of them by some positive integer number of centimeters (different sticks can be increased by a different length), but in total by at most *l* centimeters. In particular, it is allowed not to increase the length of any stick.

Determine the number of ways to increase the lengths of some sticks so that you can form from them a non-degenerate (that is, having a positive area) triangle. Two ways are considered different, if the length of some stick is increased by different number of centimeters in them.

Input

The single line contains 4 integers *a*, *b*, *c*, *l* (1 ≤ *a*, *b*, *c* ≤ 3·10^{5}, 0 ≤ *l* ≤ 3·10^{5}).

Output

Print a single integer — the number of ways to increase the sizes of the sticks by the total of at most *l* centimeters, so that you can make a non-degenerate triangle from it.

Examples

Input

1 1 1 2

Output

4

Input

1 2 3 1

Output

2

Input

10 2 1 7

Output

0

Note

In the first sample test you can either not increase any stick or increase any two sticks by 1 centimeter.

In the second sample test you can increase either the first or the second stick by one centimeter. Note that the triangle made from the initial sticks is degenerate and thus, doesn't meet the conditions.

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: May/21/2018 19:56:54 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|