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<stdio.h>
#include<stdlib.h>
#include<string.h>
#include<math.h>
#include<algorithm>
#include<queue>
#include<set>
#include<map>
#include<iostream>
using namespace std;
#define ll long long
#define REP(a,b,c) for(int a=b;a<=c;a++)
#define re register
#define int ll
#define file(a) freopen(a".in","r",stdin);freopen(a".out","w",stdout)
inline int gi(){
	int f=1,sum=0;char ch=getchar();
	while(ch>'9' || ch<'0'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0' && ch<='9'){sum=(sum<<3)+(sum<<1)+ch-'0';ch=getchar();}
	return f*sum;
}
const int N=100010,Mod=1e9+7;
int n,A,B,a[N],f[N],s[N];
signed main(){
	n=gi();A=gi();B=gi();if(A>B)swap(A,B);
	for(int i=1;i<=n;i++)a[i]=gi();
	for(int i=1;i<n-1;i++)
		if(a[i+2]-a[i]<A)return puts("0"),0;
	f[0]=s[0]=1;int mx=0,mn=0;
	for(int i=1;i<=n;i++){
		while(mx<i && a[i]-a[mx+1]>=B)mx++;
		if(mn<=mx)f[i]=(s[mx]-(mn?s[mn-1]:0)+Mod)%Mod;
		s[i]=(s[i-1]+f[i])%Mod;
		if(i>1 && a[i]-a[i-1]<A)mn=i-1;
	}
	int ans=0;
	for(int i=n;~i;i--){
		ans=(ans+f[i])%Mod;
		if(i<n && a[i+1]-a[i]<A)break;
	}
	printf("%lld\n",ans);
	return 0;
}