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>
#define ll long long
const int N=1e5+5,mo=1e9+7;
int n,i,lx,rx,ly,ry;
ll dx,dy,a[N],fx[N],gx[N],fy[N],gy[N];
ll read(){
	char c=getchar();ll k=0;for (;c<48||c>57;c=getchar());
	for (;c>47&&c<58;c=getchar()) k=(k<<3)+(k<<1)+c-48;return k;
}
int main(){
	n=read();dx=read();dy=read();
	for (i=1;i<=n;i++) a[i]=read();
	a[n+1]=2e18;fx[0]=gx[0]=fy[0]=gy[0]=1;
	for (i=1;i<=n;i++){
		if (a[i]-a[i-1]<dx) lx=i-1;
		if (a[i]-a[i-1]<dy) ly=i-1;
		for (;rx+1<i&&a[rx+1]<=a[i+1]-dy;rx++);
		for (;ry+1<i&&a[ry+1]<=a[i+1]-dx;ry++);
		if (lx<=rx) fx[i]=(gy[rx]-(lx?gy[lx-1]:0))%mo;
		if (ly<=ry) fy[i]=(gx[ry]-(ly?gx[ly-1]:0))%mo;
		gx[i]=(gx[i-1]+fx[i])%mo;
		gy[i]=(gy[i-1]+fy[i])%mo;
	}
	int ans=(fx[n]+fy[n])%mo;
	printf("%d",(ans+mo)%mo);
}