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.

The first and only line of input contains the four integers a, b, k, and t (1 \le a,b \le 100, 1 \le k \le 1000, 1 \le t \le 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 1000000007 (109+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.