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;

const int N=100100,mod=1000000007;
typedef long long ll;
int n,f1[N],f2[N];
ll X,Y,q1[N],q2[N]; 

int main(){
	ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
	cin>>n>>X>>Y;
	ll lst=-X-Y;
	int t1=0,w1=-1,t2=0,w2=-1;
	int res1=1,res2=0;
	for(int i=1;i<=n;++i){
		ll x;cin>>x;
		for(;t1<=w1&&x-q1[t1]>=X;++t1)res1=(res1+f1[t1])%mod;
		for(;t2<=w2&&x-q2[t2]>=Y;++t2)res2=(res2+f2[t2])%mod;
		int u=res1,v=res2;
		if(x-lst<X)t2=w2+1,res2=0;
		if(x-lst<Y)t1=w1+1,res1=0;
		++w1;q1[w1]=lst;f1[w1]=v;
		++w2;q2[w2]=lst;f2[w2]=u;
		lst=x;
	}
	for(;t1<=w1;++t1)res1=(res1+f1[t1])%mod;
	for(;t2<=w2;++t2)res2=(res2+f2[t2])%mod;
	cout<<(res1+res2)%mod<<'\n';
	return 0;
}