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 <vector>
#include <algorithm>
#include <map>
using namespace std;
#define rep(i,n)	for(int i=0;i<n;i++)
typedef long long ll;
ll mod=1e9+7;
ll dp[114514];//dp[i]:最後にYに入れたのがiの通り数

int main(){
	ll n,a,b;	cin>>n>>a>>b;
	if(a>b)	swap(a,b);
	vector<ll> s(n);
	rep(i,n)	cin>>s[i];
	n;
	s.insert(s.begin(),-1e18);
	for(int i=2;i<=n;i++){
		if(s[i]-s[i-2]<a){
			cout<<0<<endl;
			return 0;
		}
	}

	int t=0,zero=0;
	ll sum=0;
	dp[0]=dp[1]=1;
	for(int i=2;i<=n;i++){
		if(s[i]-s[i-1]>=a){
			while(s[i]-s[t]>=b)	sum=(sum+dp[t++])%mod;
			dp[i]=sum;
		}
		else{
			while(s[i]-s[t]>=b)	sum=(sum+dp[t++])%mod;
			dp[i]=sum;
			while(zero<i-1){
				if(zero<t)	sum=(sum+mod-dp[zero])%mod;
				dp[zero++]=0;
			}
		}
	}
	ll ret=0;
	rep(i,n+1)	ret=(ret+dp[i])%mod;
	cout<<ret<<endl;
	return 0;
}