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 int ll;

ll dp[100010],pre[100010];
const int mod = 1e9+7;
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);
	vector<ll> v(n+1,-4e18);
	for(int i=1;i<=n;i++)
		cin>>v[i];
	dp[0]=1;
	pre[0]=1;
	int from=0;
	for(int i=1;i<=n;i++){
		int to=upper_bound(v.begin(),v.end(),v[i]-B)-v.begin()-1;
		if(from<=to){
			dp[i]=(dp[i]+pre[to])%mod;
			if(from!=0)
				dp[i]=(dp[i]+mod-pre[from-1])%mod;
		}
		if(i!=n&&v[i+1]-v[i-1]<A)	dp[i]=0;
		pre[i]=(pre[i-1]+dp[i])%mod;
		if(v[i]-v[i-1]<A)	from=i-1;
	}
	ll ans=0;
	for(int i=from;i<=n;i++){
		if(i!=0&&i!=n&&v[i+1]-v[i-1]<A);
		else
			ans=(ans+dp[i])%mod;
	}
	cout<<ans<<endl;
}