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 <stdio.h>
#include <stdlib.h>
#include <algorithm>
#define p 1000000007
using namespace std;

int n,i,j,k,l,r,q,ans;
int Next[100005],f[100005],g[100005];
long long a[100005],A,B;

void add(int &a,int b){a+=b;if(a>=p)a-=p;}

int main()
{
	scanf("%d%lld%lld",&n,&A,&B);
	for(i=1;i<=n;++i)scanf("%lld",&a[i]);
	if(A<B)swap(A,B);
	Next[n]=n;
	for(i=n-1;i>=1;--i)
	if(a[i+1]-a[i]>=B)Next[i]=Next[i+1];
	else Next[i]=i;
	g[1]=1;g[Next[1]+2]=p-1;
	if(Next[1]==n)ans=1;
	for(i=1;i<=n;++i)
	{
		add(g[i],g[i-1]);
		add(f[i],g[i]);
		if(i<n)
		{
			if(i==1||a[i+1]-a[i-1]>=B)
			{
				for(;q<=n&&a[q]-a[i]<A;++q);
				l=q;r=Next[i+1]+1;
				if(l<=r)
				{
					add(g[l],f[i]);
					add(g[r+1],p-f[i]);
				}
			}
		}
		if((i==n||i==1||a[i+1]-a[i-1]>=B)&&(i==n||Next[i+1]==n))add(ans,f[i]);
	}
	printf("%d\n",ans);
}