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.
#include <bits/stdc++.h>
using namespace std;
const int MOD = 1000 * 1000 * 1000 + 7;
const int MAXDIFF = 200 * 1000 + 200;
int dp[2 * MAXDIFF + 1];
int sums[2 * MAXDIFF + 1];
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cout.precision(15);
  cout.setf(ios::fixed);
  int a, b, k, t;
  cin >> a >> b >> k >> t;
  dp[MAXDIFF + a - b] = 1;
  for (int tt = 0; tt < 2 * t; tt++) {
    for (int i = 0; i <= 2 * MAXDIFF; i++) {
      sums[i] = 0;
    }
    for (int i = 0; i <= 2 * MAXDIFF; i++) {
      sums[i] = dp[i];
      if (i > 0) {
        sums[i] += sums[i - 1];
        if (sums[i] >= MOD) sums[i] -= MOD;
      }
    }
    for (int i = 0; i <= 2 * MAXDIFF; i++) {
      int L = max(0, i - k);
      int R = min(2 * MAXDIFF, i + k);
      dp[i] = sums[R];
      if (L > 0) {
        dp[i] -= sums[L - 1];
        if (dp[i] < 0) dp[i] += MOD;
      }
    }
  }
  int ans = 0;
  for (int i = MAXDIFF + 1; i <= 2 * MAXDIFF; i++) {
    ans += dp[i];
    if (ans >= MOD) ans -= MOD;
  }
  cout << ans << endl;
}
