There is a set consisting of ~N~ distinct integers. The ~i^{th}~ smallest element in this set is ~S_i~. We want to divide this set into two sets, ~X~ and ~Y~, such that:

• The absolute difference of any two distinct elements in ~X~ is ~A~ or greater.
• The absolute difference of any two distinct elements in ~Y~ is ~B~ or greater.

How many ways are there to perform such a division, modulo ~10^9+7~? Note that ~X~ or ~Y~ may be empty.

Input Specification

The first line will contain three integers, ~N, A, B~ ~(1 \le N \le 10^5, 1 \le A, B \le 10^9)~.

The next ~N~ lines will each contain one integers, ~S_i~ ~(0 \le S_i \le 10^{15}, S_i < S_{i+1})~.

Output Specification

Print the number of different divisions satisfying the conditions, modulo ~10^9+7~.

Subtasks

For 2/15 of the points, ~N \le 20~.

For an additional 5/15 of the points, ~N \le 1000~.

Sample Input 1

5 3 7
1
3
6
9
12

Sample Output 1

5

Sample Input 2

7 5 3
0
2
4
7
8
11
15

Sample Output 2

4

Sample Input 3

8 2 9
3
4
5
13
15
22
26
32

Sample Output 3

13