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 <iostream>
#include <algorithm>
#include <vector>
#include <cstring>
#include <cstdio>
#define LL long long
#define pb push_back
#define mp make_pair
#define INF (LL)(4e18)
#define F first
#define S second
#define rep(i,a,b) for(int i=(a);i<=(b);i++)
#define per(i,b,a) for(int i=(b);i>=(a);i--)
#define forn(i,n) rep(i,1,n)
#define rep0(i,n) rep(i,0,n-1)
using namespace std;
typedef pair<int,int>pii;
#define mod 1000000007
using namespace std;
int n,f[100010],s[100010];
LL a,b,x[100010];
int get(int l,int r){
	if(l>r)return 0;
	if(!l)return s[r];
	else return (s[r]-s[l-1]+mod)%mod;
}
int main(){
	cin>>n>>a>>b;
	if(a<b)swap(a,b);
	for(int i=1;i<=n;i++)cin>>x[i];
	x[0]=-INF,x[n+1]=INF;
	f[0]=s[0]=1;
	int l=0,r=0;
	for(int i=1;i<=n+1;i++){
		while(r+1<i&&x[i]-x[r+1]>=a)r++;
		if(i>=2&&x[i-1]-x[i-2]<b)l=i-2;
		if(x[i]-x[i-1]>=a)f[i]=f[i-1];
		f[i]=(f[i]+get(l,min(i-2,r)))%mod;
		s[i]=s[i-1];
		if(x[i+1]-x[i-1]>=b)s[i]=(s[i]+f[i])%mod;
	}
	cout<<f[n+1]<<endl;
}