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<cstring>
#include<cstdio>
#include<cmath>
#include<iostream>
#define N 110000
#define mmod 1000000007
#define LL long long
using namespace std;
int n,f[N],g[N],na[N],nb[N],ca[N],cb[N],ans;
LL s[N],a,b,inf;
int main()
{
	inf=1e9;inf*=inf;
	scanf("%d%lld%lld",&n,&a,&b);
	for(int i=1;i<=n;i++) scanf("%lld",&s[i]);
	s[++n]=inf;
	na[n]=nb[n]=n;
	int j=n;
	for(int i=n-1;i>=1;i--)
	{
		while(s[j-1]-s[i]>=a) j--;
		na[i]=j;
	}
	j=n;
	for(int i=n-1;i>=1;i--)
	{
		while(s[j-1]-s[i]>=b) j--;
		nb[i]=j;
	}
	ca[n]=cb[n]=n;
	for(int i=n-1;i>=1;i--)
	{
		if(s[i+1]-s[i]>=a) ca[i]=ca[i+1];
		else ca[i]=i;
		if(s[i+1]-s[i]>=b) cb[i]=cb[i+1];
		else cb[i]=i;
	}
	s[0]=-inf;f[0]=g[0]=1;f[1]=g[1]=-1;
	for(int i=0;i<n;i++)
	{
		int l=max(i+1,na[i]-1),r=cb[i+1];
		if(l<=r) g[l]=(g[l]+f[i])%mmod,g[r+1]=(g[r+1]-f[i])%mmod;
		
		l=max(i+1,nb[i]-1);r=ca[i+1];
		if(l<=r) f[l]=(f[l]+g[i])%mmod,f[r+1]=(f[r+1]-g[i])%mmod;
		f[i+1]=(f[i+1]+f[i])%mmod;g[i+1]=(g[i+1]+g[i])%mmod;
	}
	ans=(f[n-1]+g[n-1])%mmod;
	ans=(ans+mmod)%mmod;
	printf("%d\n",ans);
	return 0;
}