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>
typedef long long i64;
const int N=1e5+7,P=1e9+7;
i64 A,B,v[N];
int n,d1=0,d2=0;
int f1[N],f2[N];
int main(){
	scanf("%d%lld%lld",&n,&A,&B);
	for(int i=1;i<=n;++i)scanf("%lld",v+i);
	int p1=0,p2=0,s1=1,s2=1;
	f1[0]=f2[0]=1;
	for(int i=1;i<n;++i){
		while(v[i+1]-v[p1+1]>=A)s1=(s1+f2[++p1])%P;
		while(v[i+1]-v[p2+1]>=B)s2=(s2+f1[++p2])%P;
		f1[i]=s1;
		f2[i]=s2;
		if(p1!=i){
			for(int j=d1;j<i;++j){
				if(j<=p2)s2=(s2-f1[j])%P;
				f1[j]=0;
			}
			d1=i;
		}else s1=(s1+f2[i])%P;
		if(p2!=i){
			for(int j=d2;j<i;++j){
				if(j<=p1)s1=(s1-f2[j])%P;
				f2[j]=0;
			}
			d2=i;
		}else s2=(s2+f1[i])%P;
	}
	while(p1<n)s1=(s1+f2[++p1])%P;
	while(p2<n)s2=(s2+f1[++p2])%P;
	printf("%d\n",((s1+s2)%P+P)%P);
	return 0;
}