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 <cstdio>
#include <cstdlib>
#include <cstring>
#include <iostream>
#include <algorithm>
typedef long long ll ;
#define rep(i, a, b) for (int i = a; i <= b; ++ i) 
const int N = 200005, mo = 1000000007 ;
using namespace std ;

int n, d[2][N], f[2][N] ; 
ll A, B, a[N] ;

int main() {
	scanf("%d%lld%lld", &n, &A, &B) ;
	rep(i, 1, n) {
		scanf("%lld", &a[i]) ;
	}
	f[0][0] = f[1][0] = 1 ;
	d[0][++ d[0][0]] = 0 ;
	d[1][++ d[1][0]] = 0 ;
	int l[2] = {0} ;
	rep(i, 2, n) {
		for ( ; l[0] < i - 2 && a[i] - a[l[0] + 1] >= A ; ++ l[0]) ;
		for ( ; l[1] < i - 2 && a[i] - a[l[1] + 1] >= B ; ++ l[1]) ;
		f[0][i - 1] = f[1][l[0]] ;
		f[1][i - 1] = f[0][l[1]] ;
		if (a[i] - a[i - 1] < A) {
			for ( ; d[0][0] ; -- d[0][0]) f[0][d[0][d[0][0]]] = 0 ;
		}
		if (a[i] - a[i - 1] < B) {
			for ( ; d[1][0] ; -- d[1][0]) f[1][d[1][d[1][0]]] = 0 ;
		}
		f[0][i - 1] = (f[0][i - 1] + f[0][i - 2]) % mo ;
		f[1][i - 1] = (f[1][i - 1] + f[1][i - 2]) % mo ;
		d[0][++ d[0][0]] = i - 1 ;
		d[1][++ d[1][0]] = i - 1 ;
	}
	printf("%d\n", (f[0][n - 1] + f[1][n - 1]) % mo) ;
	return 0 ;
}