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>
const long long MODULO = 1000 * 1000 * 1000 + 7;
const long long MIN_SOMME = -100 * 1000;
const long long MAX_SOMME = +100 * 1000;
const long long NB_SOMMES = MAX_SOMME - MIN_SOMME + 1;
long long scoreA, scoreB, taille, nbTours;
long long nbPossibilites[2][NB_SOMMES];
inline long long mod(long long a) { return (a % MODULO + MODULO) % MODULO; }
void calculerNbPossibilites() {
  for (long long somme = 0; somme < NB_SOMMES; somme++)
    nbPossibilites[0][somme] = 0;
  nbPossibilites[0][0 - MIN_SOMME] = 1;
  for (long long tour = 0; tour < nbTours; tour++) {
    long long sommePossibilites = 0;
    for (long long delta = 0; delta <= taille; delta++)
      if (delta < NB_SOMMES)
        sommePossibilites =
            mod(sommePossibilites + nbPossibilites[tour % 2][delta]);
    for (long long somme = 0; somme < NB_SOMMES; somme++) {
      nbPossibilites[(tour + 1) % 2][somme] = sommePossibilites;
      if (0 <= somme - taille)
        sommePossibilites =
            mod(sommePossibilites - nbPossibilites[tour % 2][somme - taille]);
      if (somme + taille + 1 < NB_SOMMES)
        sommePossibilites = mod(sommePossibilites +
                                nbPossibilites[tour % 2][somme + taille + 1]);
    }
  }
}
int main() {
  scanf("%lld%lld%lld%lld", &scoreA, &scoreB, &taille, &nbTours);
  calculerNbPossibilites();
  long long totalPossibilites = 0;
  long long sommeB = MIN_SOMME;
  long long sommePossibilites = 0;
  for (long long sommeA = MIN_SOMME; sommeA <= MAX_SOMME; sommeA++) {
    while (sommeB <= MAX_SOMME && scoreA + sommeA > scoreB + sommeB) {
      sommePossibilites = mod(sommePossibilites +
                              nbPossibilites[nbTours % 2][sommeB - MIN_SOMME]);
      sommeB++;
    }
    totalPossibilites = mod(totalPossibilites +
                            nbPossibilites[nbTours % 2][sommeA - MIN_SOMME] *
                                sommePossibilites);
  }
  printf("%lld", totalPossibilites);
  return 0;
}
