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<iostream>
#define I(i,n)for(int i=0;i<n;i++)
long long M=1e9+7,n,a[2],s[100000],w[2][100001],e[2],l[2][100000],p,v[2];
int main(){
	std::cin>>n>>a[0]>>a[1];
	I(i,n)std::cin>>s[i];
	I(k,2){
		p=0;
		I(i,n){
			while(s[i]-s[p]>=a[k]&&p<i-1)p++;
			l[k][i]=p;
		}
	}
	I(k,2){e[k]=-1;w[k][0]=1;}
	I(i,n){if(i){
		I(k,2)v[k]=(e[1-k]<l[k][i]?w[1-k][l[k][i]]:0);
		I(k,2)if(s[i]-s[i-1]<a[k]){e[k]=i-1;}else{(v[k]+=w[k][i-1])%=M;}
		I(k,2)w[k][i+1]=w[k][i]=v[k];
	}
	}
	std::cout<<(w[0][--n]+w[1][n])%M;
	return 0;
}