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.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;


public class Main {
	static BufferedReader in;
	static PrintWriter out;

	public static void main(String[] args) throws IOException {
		in = new BufferedReader(new InputStreamReader(System.in));
		out = new PrintWriter(System.out);

		String[]tok = rst();
		long[] d = new long[3];
		d[0] = Long.parseLong(tok[0]);
		d[1] = Long.parseLong(tok[1]);
		d[2] = Long.parseLong(tok[2]);
		long l = Long.parseLong(tok[3]);
		
		
		long total = (l+1)*(l+2)*(l+3)/6;
		for (int pos = 0; pos < 3; pos++) {
			for (int off = 0; off <= l; off++) {
				long min = Math.min((-d[0]-d[1]-d[2])+2*d[pos]+off, l-off);
				if (min<0) continue;
				total -= (min+1)*(min+2)/2L;
			}
		}
		
		out.println(total);

		in.close();
		out.close();
	}

	public static int ri() throws IOException {
		return Integer.parseInt(in.readLine());
	}

	public static long rl() throws IOException {
		return Long.parseLong(in.readLine());
	}

	public static String rs() throws IOException {
		return in.readLine();
	}

	public static String[] rst() throws IOException {
		return in.readLine().split(" ");
	}

	public static int[] rit() throws IOException {
		String[] tok = in.readLine().split(" ");
		int[] res = new int[tok.length];
		for (int i = 0; i < tok.length; i++) {
			res[i] = Integer.parseInt(tok[i]);
		}
		return res;
	}

	public static long[] rlt() throws IOException {
		String[] tok = in.readLine().split(" ");
		long[] res = new long[tok.length];
		for (int i = 0; i < tok.length; i++) {
			res[i] = Long.parseLong(tok[i]);
		}
		return res;
	}


}
