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 ll;

const int N=100005,P=1e9+7;
const ll inf=1e18;

int n,ans;
ll A,B,a[N];
int f1[N],s1[N],l1,r1;
int f2[N],s2[N],l2,r2;
inline int chk1(int x){return x>=0?s1[x]:0;}
inline int chk2(int x){return x>=0?s2[x]:0;}

int main(){
	scanf("%d%lld%lld",&n,&A,&B);
	r1=r2=s1[1]=s2[1]=f1[1]=f2[1]=1;
	scanf("%lld",&a[1]);
	for(int i=2;i<=n;i++){
		scanf("%lld",&a[i]);
		while(a[i]-a[r1]>=B)r1++;
		while(a[i]-a[r2]>=A)r2++;
		s1[i]=s1[i-1],s2[i]=s2[i-1];
		if(r2>=l2)f1[i]=(chk2(r2)-chk2(l2-1)+P)%P;
		if(r1>=l1)f2[i]=(chk1(r1)-chk1(l1-1)+P)%P;
		s1[i]=(s1[i]+f1[i])%P;
		s2[i]=(s2[i]+f2[i])%P;
		if(a[i]-a[i-1]<A)l1=i;
		if(a[i]-a[i-1]<B)l2=i;
	}
	ans+=chk1(n)-chk1(l1-1);
	ans+=chk2(n)-chk2(l2-1);
	ans=(ans%P+P)%P;
	printf("%d\n",ans);
	return 0;
}