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 division, modulo 10^9 + 7? Note that one of X and Y may be empty.

Constraints

• All input values are integers.
• 1 ≦ N ≦ 10^5
• 1 ≦ A , B ≦ 10^{18}
• 0 ≦ S_i ≦ 10^{18}(1 ≦ i ≦ N)
• S_i < S_{i+1}(1 ≦ i ≦ N - 1)

Input

The input is given from Standard Input in the following format:

N A B
S_1
:
S_N

Output

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

Examples

Input

5 3 7
1
3
6
9
12

Output

5

Input

7 5 3
0
2
4
7
8
11
15

Output

4

Input

8 2 9
3
4
5
13
15
22
26
32

Output

13

Input

3 3 4
5
6
7

Output

0

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