Codeforces Round 370 (Div. 2) |
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Finished |

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combinatorics

dp

math

*2200

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D. Memory and Scores

time limit per test

2 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputMemory 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)^{2t} games in total. Since the answer can be very large, you should print it modulo 10^{9} + 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 (10^{9} + 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.

Codeforces (c) Copyright 2010-2023 Mike Mirzayanov

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