Memory and his friend Lexa are competing to get higher score in one popular computer game. Memory starts with score a and Lexa starts with score b. In a single turn, both Memory and Lexa get some integer in the range [ - k;k] (i.e. one integer among  - k, - k + 1, - k + 2, ..., - 2, - 1, 0, 1, 2, ..., k - 1, k) and add them to their current scores. The game has exactly t turns. Memory and Lexa, however, are not good at this game, so they both always get a random integer at their turn.

Memory wonders how many possible games exist such that he ends with a strictly higher score than Lexa. Two games are considered to be different if in at least one turn at least one player gets different score. There are (2k + 1)2t games in total. Since the answer can be very large, you should print it modulo 109 + 7. Please solve this problem for Memory.

Input

The first and only line of input contains the four integers a, b, k, and t (1 ≤ a, b ≤ 100, 1 ≤ k ≤ 1000, 1 ≤ t ≤ 100) — the amount Memory and Lexa start with, the number k, and the number of turns respectively.

Output

Print the number of possible games satisfying the conditions modulo 1 000 000 007 (109 + 7) in one line.

Examples

Input

1 2 2 1


Output

6


Input

1 1 1 2


Output

31


Input

2 12 3 1


Output

0

Note

In the first sample test, Memory starts with 1 and Lexa starts with 2. If Lexa picks  - 2, Memory can pick 0, 1, or 2 to win. If Lexa picks  - 1, Memory can pick 1 or 2 to win. If Lexa picks 0, Memory can pick 2 to win. If Lexa picks 1 or 2, Memory cannot win. Thus, there are 3 + 2 + 1 = 6 possible games in which Memory wins.
import java.io.IOException;
import java.io.PrintStream;
import java.util.Scanner;


public class D {

	private static Scanner in = new Scanner(System.in);
	private static PrintStream out = System.out;

	private static final long MOD = 1000000007;
	
	private static class Summer {
		private long[] sums;
		public Summer(long[] vals, long mod) {
			sums = new long[vals.length + 1];
			for (int i = 0; i < vals.length; ++i)
				sums[i + 1] = (sums[i] + vals[i])%MOD;
		}
		public long q(int x, int y) {
			x = Math.max(x, 0);
			y = Math.min(y, sums.length - 1);
			if (x > y)
				throw new RuntimeException();
			return (MOD + sums[y] - sums[x])%MOD;
		}
	}
	
	private static long[] waysToCompute(int start, int k, int t) {
		int offset = 5000 + k*t;
		long[][] dp = new long[t + 1][2*offset];
		start += offset;
		dp[0][start] = 1;
		int min = start;
		int max = start;
		long[] below = new long[2*offset];
		for (int i = 1; i <= t; ++i) {
			for (int j = min; j <= max; ++j)
				below[j] = 0;
			for (int j = min; j <= max; ++j)
				if (dp[i - 1][j] > 0)
					below[j - k] += dp[i - 1][j];
			min -= k;
			max += k;
			Summer summerBelow = new Summer(below, MOD);
			int diff = 2*k;
			for (int j = min; j <= max; ++j) {
				dp[i][j] += summerBelow.q(j - diff, j + 1);
				dp[i][j] %= MOD;
			}
		}
		return dp[t];
	}
	
	public static void main(String[] args) throws IOException {
		// read input
		int a = in.nextInt();
		int b = in.nextInt();
		int k = in.nextInt();
		int t = in.nextInt();
		// compute number of ways we can get each score
		long[] waysA = waysToCompute(a, k, t);
		long[] waysB = waysToCompute(b, k, t);
		// solve
		Summer summerA = new Summer(waysA, MOD);
		long ans = 0;
		for (int i = 0; i < waysB.length; ++i) {
			ans += waysB[i]*summerA.q(i + 1, waysB.length);
			ans %= MOD;
		}
		out.println(ans);
	}

}
