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>
using namespace std;

typedef long long s64;
#define rep(i,l,r) for(int i=l;i<=r;++i)
const int N=1e5+5,D=1e9+7;
s64 a[N],A,B;
int fa[N],fb[N],tob[N];

int main()
{
	//freopen("1.in","r",stdin);
	int n;
	cin>>n>>A>>B;
	if(A<B)swap(A,B);
	rep(i,1,n)scanf("%lld",a+i);
	a[0]=-(1e18+5);
	fa[1]=fb[1]=1;
	int j=0;
	rep(i,2,n)
	{
		tob[i]=a[i]-a[i-1]>=B?tob[i-1]:i;
		while(a[i]-a[j+1]>=A)++j;
		if(!j)
		{
			if(tob[i-1]<=1)fa[i]=1;
			else fa[i]=0;
		}
		else
		{
			if(j==i-1)fa[i]=(fa[j]+fb[j])%D;
			else 
			{
				if(tob[i-1]>j+1||a[j+1]-a[j-1]<B)fa[i]=0;
				else 
				if(a[j+1]-a[j]>=B)fa[i]=(fa[j]+fb[j])%D;
				else fa[i]=fa[j];
			}
		}
		if(a[i]-a[i-1]>=B)fb[i]=(fb[i-1]+fa[i-1])%D;
		else 
		if(a[i]-a[i-2]>=B)fb[i]=fa[i-1];
	}
	cout<<(fa[n]+fb[n])%D;
}