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>
using namespace std;
const int N=1e5+10;
const int mod=1e9+7;
typedef long long ll;
const ll Inf=4e18;
ll gi() {
    ll x=0,o=1;char ch=getchar();
    while((ch<'0'||ch>'9')&&ch!='-') ch=getchar();
    if(ch=='-') o=-1,ch=getchar();
    while(ch>='0'&&ch<='9') x=x*10+ch-'0',ch=getchar();
    return x*o;
}
int n,f[N],s[N];
ll a,b,x[N];
int getsum(int l,int r) {
    if(l>r) return 0;
    if(!l) return s[r];
    else return (s[r]-s[l-1]+mod)%mod;
}
int main() {
    cin>>n>>a>>b;
    if(a<b) swap(a,b);
    for(int i=1;i<=n;i++) x[i]=gi();
    x[0]=-Inf;x[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&&x[i]-x[r+1]>=a) r++;
        if(i>=2&&x[i-1]-x[i-2]<b) l=i-2;
        if(x[i]-x[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(x[i+1]-x[i-1]>=b) s[i]=(s[i]+f[i])%mod;
    }
    printf("%d\n",f[n+1]);
    return 0;
}
//orzgzy
//鸡贼明年进队超稳