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;
#define ll long long 
#define fr first
#define sc second
#define MAX ((ll)(1e18+100))
#define MOD ((ll)(1e9+7))
#define HSM ((ll)(307))
#define ARRS ((ll)(1e6+900))
#define pb push_back
#define mid ((l+r)>>1)
#define PI 3.14159265358979323846
#define MXN 500009

ll a[ARRS];
ll dp[ARRS];
ll s[ARRS];

int main(){
	ll n,A,B;
	cin>>n>>A>>B;
	if(A>B)swap(A,B);
	for(int i=1; i<=n; i++)
		cin>>a[i];
	ll l=0;
	a[0]=-MAX;
	dp[0]=1;
	s[0]=1;
	for(int i=1; i<=n; i++){
		ll r=upper_bound(a,a+n+1,a[i]-B)-a-1;
		if(l<=r)
			dp[i]=(4ll*MOD+s[r]-((l!=0)?s[l-1]:0))%MOD;
		if(abs(a[i]-a[i-1])<A){
			l=i-1;
			if(i!=1&&abs(a[i]-a[i-2])<A){
				cout<<0;
				return 0;
			}
		}

		s[i]=(s[i-1]+dp[i])%MOD;
	}
	ll pas=0;
	for(int i=l; i<=n; i++){
		pas+=dp[i];
	}
	cout<<pas%MOD;
}