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>
using namespace std;

typedef long long ll;
const int MAXN=1e5+5;
const int MOD=1e9+7;
const ll INF=2e18;

ll n,A,B;
ll a[MAXN],f[MAXN],s[MAXN];

ll getsum(int l,int r){
    if(l>r) return 0;
    if(!l) return s[r];
    return ((s[r]-s[l-1])%MOD+MOD)%MOD;
}

int main(){

    scanf("%lld%lld%lld",&n,&A,&B);
    if(A<B) swap(A,B);
    for(int i=1;i<=n;i++) scanf("%lld",&a[i]);
    a[0]=-INF,a[n+1]=INF;
    f[0]=s[0]=1;
    int l=0,r=0;
    for(int i=1;i<=n+1;i++){
        while(r+1<i&&a[i]-a[r+1]>=A) r++;
        if(i>=2&&a[i-1]-a[i-2]<B) l=i-2;
        if(a[i]-a[i-1]>=A) f[i]=f[i-1];
        f[i]=(f[i]+getsum(l,min(i-2,r)))%MOD;
        s[i]=s[i-1];
        if(a[i+1]-a[i-1]>=B) s[i]=(f[i]+s[i])%MOD;
    }
    printf("%lld",f[n+1]);

    fclose(stdin);
    fclose(stdout);
}