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<iostream>
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>

using namespace std;

typedef long long ll;

inline ll read()
{
	ll x=0;char ch=getchar();
	while(ch<'0' || '9'<ch)ch=getchar();
	while('0'<=ch && ch<='9')x=x*10+(ch^48),ch=getchar();
	return x;
}

const int N=1e5+9;
const int md=1e9+7;

ll n,x[N],a[2],p[2],sp[2];
ll f[N][2],sumf[N][2];

int main()
{
	n=read();
	a[0]=read();a[1]=read();

	for(int i=1;i<=n;i++)
		x[i]=read();
	x[0]=-1e18;

	p[0]=p[1]=sp[0]=sp[1]=0;
	f[0][0]=f[0][1]=sumf[0][0]=sumf[0][1]=1;
	for(int i=1;i<n;i++)
	{
		for(int j=0;j<=1;j++)
		{
			while(p[j]<i && x[i+1]-x[p[j]]>=a[j])
				p[j]++;
			f[i][j]=sumf[p[j]-1][j^1];
		}
		for(int j=0;j<=1;j++)
		{
			if(x[i+1]-x[i]<a[j])
				for(;sp[j]<i;sp[j]++)
					f[sp[j]][j]=sumf[sp[j]][j]=0;
			sumf[i][j]=(sumf[i-1][j]+f[i][j])%md;
		}
	}

	printf("%lld\n",(sumf[n-1][0]+sumf[n-1][1])%md);
	return 0;
}