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 int long long 
#define re register int 
#define il inline
#define ll long long
using namespace std;
const int inf=1e9;
il int read(){
	char c=getchar();int z=0,f=1;
	while(c!='-'&&(c>'9'||c<'0')) c=getchar();
	if(c=='-') f=-1,c=getchar();
	while(c>='0'&&c<='9') z=(z<<1)+(z<<3)+c-'0',c=getchar();
	return z*f;
}
const int N=1e5+10;
const int mod=1e9+7;
int n,A,B;
int f[N],sum[N],a[N];
signed main (){
	n=read();A=read();B=read();
	if(A<B) swap(A,B);
	for(re i=1;i<=n;i++) a[i]=read();
	for(re i=1;i+2<=n;i++) 
		if(a[i+2]-a[i]<B){cout<<0;return 0;}
	f[0]=sum[0]=1;
	for(re i=1,p=0,q=0;i<=n;i++){
		while(q<i&&a[i]-a[q+1]>=A) ++q;
		if(p<=q)f[i]=(f[i]+sum[q]-(p?sum[p-1]:0)+mod)%mod;
		sum[i]=(sum[i-1]+f[i])%mod;
		if(i>1&&a[i]-a[i-1]<B) p=i-1;
	}
	int ans=0;
	for(re i=n;i>=0;i--){
		ans=(ans+f[i])%mod;
		if(i<n&&a[i+1]-a[i]<B) break;
	}
	cout<<ans;
	return 0;
}