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>
#define int long long int
using namespace std;
const int INF = 3e18;
const int MOD = 1e9 + 7;

int n, a, b, s[100010];

queue<int> qx, qy;
int dpx[100010], dpy[100010];

signed main()
{
  cin >> n >> a >> b;
  for(int i = 1; i <= n; i++)
    cin >> s[i];

  s[0] = -INF, s[n + 1] = INF, dpx[0] = 1;

  for(int i = 1; i <= n; i++){

    if(s[i] - s[i - 1] >= a)
      dpx[i] += dpx[i - 1];
    else
      while(!qx.empty())
	qx.pop();
    if(s[i] - s[i - 1] >= b)
      dpy[i] += dpy[i - 1];
    else
      while(!qy.empty())
	qy.pop();

    qx.push(i - 1);
    qy.push(i - 1);
    
    while(!qx.empty() && s[i + 1] - s[qx.front()] >= b){
      dpx[i] += dpy[qx.front()];
      qx.pop();
    }
    while(!qy.empty() && s[i + 1] - s[qy.front()] >= a){
      dpy[i] += dpx[qy.front()];
      qy.pop();
    }

    dpx[i] %= MOD;
    dpy[i] %= MOD;

  }

  cout << (dpx[n] + dpy[n]) % MOD << endl;
  return 0;
}