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.util.*;
import java.io.*;
public class Morphius {
    static long mod = 1000_000_007L;
    static long[][] calc(int a,int t,int k){
        long dp[][] = new long[t + 1][t*k + t*k + 200];
        int zero = t*k;
        dp[0][zero + a] = 1;
        for(int i = 0;i < t;i++){
            for(int j = 0;j < dp[0].length;j++){
                if(dp[i][j] == 0)continue;
                dp[i + 1][j - k] += dp[i][j];
                    dp[i + 1][j + k + 1] -= dp[i][j];
            }
            for(int j = 1;j < dp[0].length;j++){
                dp[i + 1][j] += dp[i + 1][j - 1];
                dp[i + 1][j] %= mod;
                dp[i + 1][j] = (dp[i + 1][j] + mod) % mod;
            }
        }
        return dp;
    }
    public static void main(String[] args) throws Exception {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        StringTokenizer st = new StringTokenizer(br.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());
        long dp1[][] = calc(a, t, k);
        long dp2[][] = calc(b, t, k);
        long ans = 0;
        long curr = 0;
        for (int i = 1; i < dp1[0].length; i++) {
            //System.out.println(dp1[t][i]);
            dp2[t][i - 1] %= mod;
            dp1[t][i] %= mod;
            curr += dp2[t][i - 1];
            ans += dp1[t][i] * curr;
            ans %= mod;
            while(curr >= mod)curr -= mod;
        }
        System.out.print(ans);
    }
}