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>
#define LL long long
#define N 100005
#define INF (1LL<<60)
using namespace std;
const int mo=1e9+7;
int n,f[N],g[N],a[N],b[N]; LL A,B,S[N];
int find(int x,int *P){ return P[x] ? P[x]=find(P[x],P) : x;}
int main()
{
	int i,p,q;
	cin>>n>>A>>B;
	for(i=1;i<=n;i++){
		scanf("%lld",&S[i]);
		if(S[i]-S[i-1]>=A) a[i]=find(i-1,a);
		if(S[i]-S[i-1]>=B) b[i]=find(i-1,b);
	  }
	f[1]=g[1]=1,S[p=q=0]=-INF;
	for(i=2;i<=n;i++){
		while(p+1<=i&&S[p+1]+A<=S[i]) p++;
		if(p==i-1) f[i]=f[i-1];
		if(p>=find(i-1,b)-1)
			f[i]=(f[i]+g[min(p+1,i-1)])%mo;
		while(q+1<=i&&S[q+1]+B<=S[i]) q++;
		if(q==i-1) g[i]=g[i-1];
		if(q>=find(i-1,a)-1)
			g[i]=(g[i]+f[min(q+1,i-1)])%mo;
	  }
	printf("%d",(f[n]+g[n])%mo);
	return 0;
}