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>
#define F first
#define S second
#define X real()
#define Y imag()
using namespace std;
typedef long long ll;
typedef long double ld;
const ll mod=1e9+7;

const int N=1<<17;
ll st[2*N];

void add(int i, ll v){
	for (i+=N;i;i/=2) {
		st[i]+=v;
		st[i]%=mod;
	}
}

ll sum(int a, int b){
	a+=N;
	b+=N;
	ll s=0;
	while (a<=b){
		if (a%2) s+=st[a++];
		if (!(b%2)) s+=st[b--];
		a/=2;
		b/=2;
		s%=mod;
	}
	return s;
}

ll s[101010];
ll vv[101010];

int main(){
	ios_base::sync_with_stdio(0);
	cin.tie(0);
	int n;
	ll a,b;
	cin>>n>>a>>b;
	if (a>b) swap(a, b);
	for (int i=1;i<=n;i++){
		cin>>s[i];
		if (i>=3&&s[i]-s[i-2]<a){
			cout<<0<<endl;
			return 0;
		}
	}
	int lp=0;
	int hp=0;
	add(0, 1);
	for (int i=1;i<=n;i++){
		if (i-2>=1&&(s[i-1]-s[i-2])<a){
			lp=i-2;
		}
		while (s[i]-s[hp+1]>=b){
			hp++;
		}
		ll tv=sum(lp, hp);
		add(i, tv);
	}
	if (n-1>=1&&s[n]-s[n-1]<a){
		lp=n-1;
	}
	cout<<sum(lp, n)<<endl;
}