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;
typedef long long ll;
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
ll ans = 0;
const ll mo = 1000000007;
const ll INF = 1LL << 62; //MAX 9223372036854775807
int main()
{
ll n , a , b ;
cin >> n >> a >> b ;
if(a>b)swap(a,b);
vector<ll> s(n+1);
s[0]=-1LL*INF;
rep(i, n){
  cin >> s[i+1];
}
rep(i,n-1){
  if(s[i+2]-s[i]<a){
    cout << 0 << endl;
    return 0;
  }
}
vector<ll> v(n+1);
ll sum=1,st=0,en=1;
v[0]=1;v[1]=1;
for(ll i=2;i<=n;i++){
  while(s[en]<=s[i]-b){
    sum+=v[en];
    sum%=mo;
    en++;
  }
  v[i]=sum;
  if(s[i-1]>s[i]-a){
    while(1){
      if(st!=en){
        sum-=v[st];
        sum%=mo;
      }
      v[st]=0;
      st++;
      if(st>en)en++;
      if(st==i-1)break;
    }
  }
}
for(auto an:v)ans=(ans+an+mo)%mo;;
cout << ans << endl;
return 0;
}