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;
#define mod 1000000007
#define pb push_back
#define rep(i,x) for(int i=0;i<x;i++)
ll dpa[100005],dpb[100005],a,b,x[1000005],ruia[100005],ruib[100005];
int n;
int la,ra,lb,rb;
int main(){
	scanf("%d%lld%lld",&n,&a,&b);
	for(int i=1;i<=n;i++){
		scanf("%lld",&x[i]);
	}
	dpa[0] = 1; dpb[0] = 1;
	ruia[0] = 1; ruib[0] = 1;
	for(int i=2;i<=n;i++){
		int id = upper_bound(x+1,x+n+1,x[i]-a)-x;
		//[lb,min(rb,id-1)]
		int R = min(rb,id-1);
		if(lb<=R) dpa[i-1] = (ruib[R]-ruib[lb-1]+mod)%mod;
		ruia[i-1] = (ruia[i-2]+dpa[i-1])%mod;
		id = upper_bound(x+1,x+n+1,x[i]-b)-x;
		//[la,min(ra,id-1)]
		R = min(ra,id-1);
		if(la<=R) dpb[i-1] = (ruia[R]-ruia[la-1]+mod)%mod;
		ruib[i-1] = (ruib[i-2]+dpb[i-1])%mod;
		ra++; rb++;
		if(x[i]-x[i-1]<a){
			la = ra;
		}
		if(x[i]-x[i-1]<b){
			lb = rb;
		}
	}
	ll ans = 0;
	for(int i=la;i<=ra;i++) ans+=dpa[i];
	for(int i=lb;i<=rb;i++) ans+=dpb[i];
	cout<<ans%mod<<endl;
}