Sheldon and Leonard are playing a game. Thay starts with score a and b respectively.

In a single turn, both of them picks a integer from [ - k , k ].

They always get a random integer at their turn.

The game has t turns.

Sheldon wants to know that in how many games he ends up with higher score then Leonard.

Since the answer can be very large, you should print it modulo 10^9 + 7.

Input -

• The first line contains integers a, b, k, and t .

Output-

• Print number of games (Sheldon ends up with higher score than Leonard) modulo 1000000007.

Constraints -

• 1 ≤ a , b ≤ 100
• 1 ≤ k ≤ 1000
• 1 ≤ t ≤ 100