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 int uli;
const int mx=1e5+10;
const uli mod=1e9+7;
uli f[mx][2];
int nxt[mx][2]; 
uli x[mx];
int main(){
  int n;
  uli step[2];
  scanf("%d %lld %lld",&n,step,step+1); 
  for(int i=1;i<=n;i++)scanf("%lld",x+i);
  sort(x,x+n+1);
  nxt[n][0]=nxt[n][1]=1;
  for(int i=n-1;i>=0;i--){
    for(int it=0;it<2;it++){
      nxt[i][it]=1;
      if(x[i+1]-x[i]>=step[it]){
        nxt[i][it]+=nxt[i+1][it];
      }
    }
  }
  x[0]=-2e18;
  sort(x,x+n+1);
  f[n+1][0]=f[n+1][1]=1;
  for(int i=n;i>=1;i--){
    for(int b=0;b<2;b++){
      int idx=lower_bound(x,x+n+1,x[i-1]+step[b])-x;
      if(idx==i){
        f[i][b]+=f[i+1][b];
        f[i][b]+=f[i+1][b^1];
      }
      else if(nxt[i][b^1]>=idx-i){
        f[i][b]+=f[idx][b^1];
      }
      f[i][b]%=mod;
    }
  }
  printf("%lld\n",f[1][0]);
  return 0;
}