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 L long long
using namespace std;
const int q=1000000007;
int n,u[100010],v[100010];
L a,b,x[100010];
struct dp
{
    int a[100010],b[100010],t;
    inline int& operator[](int i)
    {
        if(b[i]<t)
          b[i]=t,a[i]=0;
        return a[i];
    }
}f,g;
int main()
{
	//freopen(".in","r",stdin);
	//freopen(".out","w",stdout);
	int i,j,k;
	scanf("%d%lld%lld",&n,&a,&b);
	for(i=1,j=0,k=0;i<=n;i++)
	  {
	   scanf("%lld",&x[i]);
	   while(x[i]-x[j+1]>=a)
	     j++;
	   while(x[i]-x[k+1]>=b)
	     k++;
	   u[i]=j;
	   v[i]=k;
      }
    f[0]=g[0]=1;
    for(i=0;i<n;i++)
     f.b[i]=g.b[i]=i+1;
    for(i=2;i<=n;i++)
      {
       f[i-1]=g[min(u[i],i-2)];
       g[i-1]=f[min(v[i],i-2)];
       if(u[i]<i-1)
         f.t=i;
       if(v[i]<i-1)
         g.t=i;
       f[i-1]=(f[i-1]+f[i-2])%q;
       g[i-1]=(g[i-1]+g[i-2])%q;
      }
    printf("%d\n",(f[n-1]+g[n-1])%q);
	return 0;
}