You 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 ≤ 3·105, 0 ≤ l ≤ 3·105).

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.
import java.io.BufferedOutputStream;
import java.io.BufferedReader;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

public class C
{
	public static final Random RANDOM = new Random(System.currentTimeMillis());
	private BufferedReader bufferedReader;
	private StringTokenizer stringTokenizer;
	private PrintWriter out;

	public C()
	{
		this(new BufferedReader(new InputStreamReader(System.in)));
	}

	public C(BufferedReader bufferedReader)
	{
		this.bufferedReader = bufferedReader;
		this.stringTokenizer = null;
		this.out = new PrintWriter(new BufferedOutputStream(System.out));
	}

	public C(String file) throws FileNotFoundException
	{
		this(new BufferedReader(new InputStreamReader(new FileInputStream(file))));
	}

	private String next() throws IOException
	{
		while ((this.stringTokenizer == null) || (!this.stringTokenizer.hasMoreTokens()))
		{
			this.stringTokenizer = new StringTokenizer(this.bufferedReader.readLine());
		}
		return stringTokenizer.nextToken();
	}

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

	public double nextDouble() throws IOException
	{
		return Double.parseDouble(next());
	}

	public long nextLong() throws IOException
	{
		return Long.parseLong(next());
	}

	public String nextLine() throws IOException
	{
		return this.bufferedReader.readLine();
	}

	public void close()
	{
		out.close();
	}

	public static void main(String[] args)
	{
		C template = new C();
		try
		{
			template.solve();
		}
		catch (IOException exception)
		{
			exception.printStackTrace();
		}
		template.close();
	}

	public static boolean degenerate(int[] x)
	{
		boolean result = false;
		for (int index = 0; index < 3; index++)
		{
			result |= x[index] >= x[(index + 1) % 3] + x[(index + 2) % 3];
		}
		return result;
	}

	public static long sumUpTo(long n)
	{
		n = Math.max(0, n);
		return n * (n + 1) / 2;
	}

	public static long countTooLongX0(int x0, int x1, int x2, int l, int l0)
	{
		return sumUpTo(Math.min(x0 + l0 - x1 - x2 + 1, l - l0 + 1));
	}

	public static long countTooLongX1(int x0, int x1, int x2, int l, int l0)
	{
		long result;
		long diff = Math.max(0, l - l0 - (x0 + l0 + x2 - x1 - 1));
		if (diff % 2 == 0)
		{
			result = sumUpTo(diff / 2) * 2;
		}
		else
		{
			result = (diff + 1) * (diff + 1) / 2 / 2;
		}
		return result;
	}

	public static long solveUnsorted(int[] x, int l)
	{
		long result = 0;
		for (int l0 = 0; l0 <= l; l0++)
		{
			result += sumUpTo(l - l0 + 1);
			result -= countTooLongX0(x[0], x[1], x[2], l, l0);
			result -= countTooLongX1(x[0], x[1], x[2], l, l0);
			result -= countTooLongX1(x[0], x[2], x[1], l, l0);
		}
		return result;
	}

	public static long solve(int[] x, int l)
	{
		Arrays.sort(x);
		return solveUnsorted(new int[]
		{ x[2], x[1], x[0] }, l);
	}

	public static long solveSlow(int x0, int x1, int x2, int l)
	{
		long result = 0;
		for (int l0 = 0; l0 <= l; l0++)
		{
			for (int l1 = 0; l1 <= l; l1++)
			{
				for (int l2 = 0; l2 <= l; l2++)
				{
					if (l0 + l1 + l2 <= l)
					{
						if (!degenerate(new int[]
						{ x0 + l0, x1 + l1, x2 + l2 }))
						{
							result += 1;
						}
					}
				}
			}
		}
		return result;
	}

	public void solve() throws IOException
	{
		int[] x = new int[3];
		x[0] = nextInt();
		x[1] = nextInt();
		x[2] = nextInt();
		int l = nextInt();
		//		for (int l2 = 0; l2 <= l; l2++)
		//		{
		//			for (int l1 = 0; l1 <= l - l2; l1++)
		//			{
		//				int x1 = Math.min(x[1] + l1, x[2] + l2);
		//				int x2 = Math.max(x[1] + l1, x[2] + l2);
		//				int l0Min = Math.max(0, x2 - x1 - x[0] + 1);
		//				int l0Max = Math.min(l - l2 - l1, x1 + x2 - x[0] - 1);
		//				result += Math.max(0, l0Max - l0Min + 1);
		//			}
		//		}
		System.out.println(solve(x, l));
	}
}