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 (2 k + 1) 2 t games in total. Since the answer can be very large, you should print it modulo 10 9 + 7 . Please solve this problem for Memory. 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. Print the number of possible games satisfying the conditions modulo 1 000 000 007 ( 10 9 + 7 ) in one line. 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.