Division into Two

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

inputFormat

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

outputFormat

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

样例

5 3 7
1
3
6
9
12

5