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<cstdio>
#include<algorithm>
#define ll long long
using namespace std;
const int N=100005,Mod=1e9+7;
int n,ans,f[N],g[N];
ll a[N],A,B;
int main()
{
	scanf("%d%lld%lld",&n,&A,&B);
    if(A>B)swap(A,B);
    for(int i=1;i<=n;i++)scanf("%lld",&a[i]);
    sort(a+1,a+n+1);
    for(int i=3;i<=n;i++)if(a[i]-a[i-2]<A){printf("0\n");return 0;}
    f[0]=g[0]=1;
	int l=0,r=0;
    for(int i=1;i<=n;i++)
    {
        while(r<i-1&&a[i]-a[r+1]>=B)++r;
        if(l<=r)f[i]=(g[r]+Mod-(l?g[l-1]:0))%Mod;
        g[i]=(g[i-1]+f[i])%Mod;
        if(i>1&&a[i]-a[i-1]<A)l=i-1;
    }
    for(int i=n;i>=0;i--)
    {
        ans=(ans+f[i])%Mod;
        if(i<n&&a[i+1]-a[i]<A)break;
    }
    printf("%d\n",ans);
    return 0;
}