Problem Statement

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 $10^9 + 7$.