Problem: 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

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
#define int long long
#define INF 2e+18
#define MOD 1000000007
using namespace std;

signed main(){
	int n,a,b,x[100001],lst1 = 0,lst2 = 0,dp1[100010] = {},dp2[100010] = {};
	cin >> n >> a >> b;
	for(int i = 0;i < n;i++) cin >> x[i];
	dp1[1] = 1;
	dp2[1] = 1;
	for(int i = 1;i < n;i++){
		int ind = min((int)(upper_bound(x,x + n,x[i] - a) - x + 1),i);
		int tmp = (dp1[i] + dp2[ind] - dp2[min(lst2,ind)] + MOD) % MOD;
		ind = min((int)(upper_bound(x,x + n,x[i] - b) - x + 1),i);
		dp2[i + 1] = (dp2[i] + dp1[ind] - dp1[min(lst1,ind)] + MOD) % MOD;
		dp1[i + 1] = tmp;
		if(x[i] - x[i - 1] < a) lst1 = i;
		if(x[i] - x[i - 1] < b) lst2 = i;
	}
	cout << (dp1[n] - dp1[lst1] + dp2[n] - dp2[lst2] + MOD * 2) % MOD << endl;
	return 0;
}