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:
// Do you knOW what it feels like?

		// To be TorTured by your own MinD?
	
	// I don't wanna feel the PAIN.

// I BeG you to KILL me, pleASE...

#include <bits/stdc++.h>
using namespace std;

#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("Os")

#define F first
#define S second
#define pb push_back
#define SZ(x) (ll)(x.size())
#define all(x) x.begin(),x.end()

typedef long long ll;
typedef pair<ll,ll> pll;
typedef long double ld;

//mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

const ll maxn=2e5+10, lg=17, mod=1e9+7, inf=1e18;

ll n,a,b,s[maxn],f[maxn];
ll ans;

int main(){
	ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);
	
	cin>>n>>a>>b;
	if(a>b) swap(a,b);
	for(int i=1;i<=n;i++) cin>>s[i];
	for(int i=2;i<n;i++) if(s[i+1]-s[i-1]<a) return cout<<0,0;
	ll j=0;
	f[0]=1, s[0]=-b;
	for(int i=1;i<=n;i++){
		while(j<i && s[i]-s[j]>=b) ans+=f[j++], ans%=mod;
		f[i]=ans;
		if(s[i]-s[i-1]<a) ans=0, j=i-1;
	}
	for(int i=j;i<=n;i++) ans+=f[i], ans%=mod;
	cout<<ans<<endl;

	return 0;
}