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>
#include<algorithm>
using namespace std;
#define MAXN 100010
#define LL long long
#define MO 1000000007
LL g[MAXN],p[MAXN],A,B,ans,a[MAXN];
int la[MAXN],lb[MAXN],ua[MAXN],ub[MAXN];
int n;
int main()
{
	scanf("%d%lld%lld",&n,&A,&B);
	n++;
	for(int i=2,j=2,k=2;i<=n;i++)
	{
		scanf("%lld",&a[i]);
		if(i==1) la[i]=i,lb[i]=i,ua[i]=0,ub[i]=0;
		else
		{
			if(a[i-1]+A<=a[i]) la[i]=la[i-1];
			else la[i]=i;
			while(a[j]+A<=a[i])	j++;
			ua[i]=j-1;
			if(a[i-1]+B<=a[i]) lb[i]=lb[i-1];
			else lb[i]=i;
			while(a[k]+B<=a[i]) k++;
			ub[i]=k-1;
		}
	}
	g[1]=1,p[1]=1;
	ua[n+1]=n-1,ub[n+1]=n-1;
	for(int i=2;i<=n;i++)
	{
		if(ub[i+1]>la[i]-2)
			g[i]=(p[min(ub[i+1],i-1)]-p[max(0,la[i]-2)]+MO)%MO;
		if(ua[i+1]>lb[i]-2)
			p[i]=(g[min(ua[i+1],i-1)]-g[max(0,lb[i]-2)]+MO)%MO;
		g[i]=(g[i]+g[i-1])%MO;
		p[i]=(p[i]+p[i-1])%MO;
	}
	ans=(g[n]-g[n-1]+MO)%MO+(p[n]-p[n-1]+MO)%MO;
	ans%=MO;
	printf("%lld\n",ans);
}