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:
//Love and Freedom.
#include<cstdio>
#include<algorithm>
#include<cstring>
#include<cmath>
#define ll long long
#define inf 20021225
#define N 100010
#define mdn 1000000007
using namespace std;
int read()
{
	int s=0,f=1; char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-') f=-1; ch=getchar();}
	while(ch>='0'&&ch<='9') s=s*10+ch-'0',ch=getchar();
	return f*s;
}
void upd(int &x,int y){x+=x+y>=mdn?y-mdn:y;}
int pre[N],n,f[N]; ll a[N],A,B;
int get(int l,int r)
{
	if(l>r)	return 0;
	return !l?pre[r]:(pre[r]-pre[l-1]+mdn)%mdn;
}
int main()
{
	int n=read(); scanf("%lld%lld",&A,&B);
	if(A<B)	swap(A,B);
	for(int i=1;i<=n;i++)	scanf("%lld",&a[i]);
	pre[0]=f[0]=1; int l=0,r=0;
	a[0]=-1e18; a[n+1]=(2e18)+1;
	for(int i=1;i<=n+1;i++)
	{
		while(r<i&&a[i]>=a[r]+A)	r++; r--;
		if(a[i]-a[i-1]>=A)	f[i]=f[i-1];
		upd(f[i],get(l,min(r,i-2)));
		pre[i]=pre[i-1];
		if(a[i+1]-a[i-1]>=B)	upd(pre[i],f[i]);
		if(a[i]-a[i-1]<B)	l=i-1;
	}
	printf("%d\n",f[n+1]);
	return 0;
}