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.BufferedReader;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.HashMap;
import java.util.Map;
import java.util.StringTokenizer;

public class R370D2P4 {

	static long MOD = (long) (1e9 + 7);

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

		// crap, this is more complicated than i thought

		// for (int i = -5; i <= 5; i++) {
		// System.out.println(waysToGet(i, 0, 1, 2));
		// }
		StringTokenizer st = new StringTokenizer(bf.readLine());
		int a = Integer.parseInt(st.nextToken());
		int b = Integer.parseInt(st.nextToken());
		int k = Integer.parseInt(st.nextToken());
		int t = Integer.parseInt(st.nextToken());

		// huh, this isn't as hard as it looks
		Map<Integer, Long> cumWaysForLexaToGet = new HashMap<Integer, Long>();
		long sum = 0;
		int minLexa = b - k * t;
		int maxLexa = b + k * t;
		for (int i = minLexa; i <= maxLexa; i++) {
			sum += waysToGet(i, b, k, t);
			sum %= MOD;
			cumWaysForLexaToGet.put(i, sum);
		}
		// System.out.println(cumWaysForLexaToGet);

		long numWays = 0;
		for (int i = a - k * t; i <= a + k * t; i++) {
			// System.out.println("ways for a to get " + i + ": " + waysToGet(i, a, k, t));
			if (i > maxLexa) {
				numWays += cumWaysForLexaToGet.get(maxLexa) * waysToGet(i, a, k, t);
				numWays %= MOD;
			} else if (i > minLexa) {
				numWays += cumWaysForLexaToGet.get(i - 1) * waysToGet(i, a, k, t);
				numWays %= MOD;
			}
		}
		System.out.println(numWays);

	}

	private static long[] convs = null;

	public static long waysToGet(int score, int offset, int k, int t) {
		if (convs == null) {
			convs = new long[2 * k + 1];
			Arrays.fill(convs, 1);
			for (int iter = 1; iter < t; iter++) {
				long[] next = new long[2 * iter * k + (2 * k + 1)];
				int sum = 0;
				for (int i = 0; i < next.length; i++) {

					int start = i - 2 * k;
					int end = i;
					if (start > 0) {
						sum -= convs[start - 1];
					}
					if (end < convs.length) {
						sum += convs[end];
					}
					sum %= MOD;
					while (sum < 0) {
						sum += MOD;
					}
					next[i] = sum;
				}

				convs = next;
			}
		}
		// System.out.println(Arrays.toString(convs));
		int idx = score - offset + k * t;
		if (idx < 0 || idx >= convs.length) {
			return 0;
		} else {
			return convs[idx];
		}
	}
}