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<cstring>
#include<algorithm>
using namespace std;
const int N=1e5+5;
typedef long long ll;
const ll mod=1e9+7;
ll n,a,b;
ll s[N];
ll f[N],g[N];
int main()
{
    //freopen("division.in","r",stdin);
    //freopen("division.out","w",stdout);
    scanf("%lld%lld%lld",&n,&a,&b);
    for(ll i=1;i<=n;i++)
        scanf("%lld",&s[i]);
    if(a>b)
        swap(a,b);
    for(ll i=3;i<=n;i++)
        if(s[i]-s[i-2]<a){
            puts("0");
            return 0;
        }
    s[0]=-2e18;
	s[n+1]=2e18;
    f[0]=g[0]=1;
    int l=0,r=0;
    for(int i=1;i<=n+1;i++){
        while(r<i-1&&s[i]-s[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&&s[i]-s[i-1]<a)
            l=i-1;
    }
    printf("%d\n",f[n+1]);
}