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.*;
import java.util.Arrays;
import java.util.StringTokenizer;

public class D {

	static final int MOD = (int)1e9 + 7;
	static final int OFFSET = 200100;

	public static void main(String[] args) throws Exception {

		Scanner sc = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);

		int a = sc.nextInt(), b = sc.nextInt(), k = sc.nextInt(), t = sc.nextInt();
		int start = -OFFSET + k, end = OFFSET - k;
		int[][] dp = new int[2][OFFSET * 2 + 1];
		for(int i = 0; i <= OFFSET; ++i)
			dp[0][i + OFFSET] = 1;
		for(int turn = 1; turn <= t * 2; ++turn)
		{
			int x = turn & 1, y = x ^ 1;
			for(int diff = -OFFSET; diff <= OFFSET; ++diff)
			{

				int l = Math.max(OFFSET + diff - k, 0), r = Math.min(OFFSET + diff + k, OFFSET * 2);
				dp[x][OFFSET + diff] = (dp[y][r] + (l == 0 ? 0 : -dp[y][l - 1] + MOD)) % MOD;
			}
			if(turn < t * 2)
				for(int i = 1; i < OFFSET * 2 + 1; ++i)
					dp[x][i] = (dp[x][i] + dp[x][i - 1]) % MOD;
		}
		int ans = 0;
		for(int diff = 1; diff <= OFFSET; ++diff)
		{
			if(diff + b - a > OFFSET)
				continue;
			if(dp[0][OFFSET + diff + b - a] != 0)

			ans += dp[0][OFFSET + diff + b - a];
			ans %= MOD;
		}
		out.println(ans);
		out.close();
	}

	static class Scanner
	{
		StringTokenizer st;
		BufferedReader br;

		public Scanner(InputStream s){	br = new BufferedReader(new InputStreamReader(s));}

		public Scanner(FileReader s) throws FileNotFoundException {	br = new BufferedReader(s);}

		public String next() throws IOException
		{
			while (st == null || !st.hasMoreTokens())
				st = new StringTokenizer(br.readLine());
			return st.nextToken();
		}

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

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

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

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

		public boolean ready() throws IOException {return br.ready();}
	}
}