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;

int N; long long A, B;
#define MAX_N 100000
long long S[MAX_N];
int FA[MAX_N], FB[MAX_N];
#define MOD 1000000007
long long X[MAX_N], Y[MAX_N];

void solve(int i, long long a, int fb[MAX_N],
  long long x[MAX_N], long long y[MAX_N]) {
  int j = upper_bound(S, S + N, S[i] - a) - S - 1;
  if(j < 0) x[i] = fb[i - 1] - fb[0] == i - 1;
  else if(j == i - 1) x[i] = (x[i - 1] + y[i - 1]) % MOD;
  else {
    if(fb[i - 1] - fb[j + 1] == (i - 1) - (j + 1)) {
      x[i] = y[j + 1];
    } else {
      x[i] = 0;
    }
  }
}
int main() {
  cin >> N >> A >> B;
  for(int i = 0; i < N; ++i) cin >> S[i];
  FA[0] = FB[0] = 0;
  for(int i = 1; i < N; ++i) {
    FA[i] = FA[i - 1] + (S[i] - S[i - 1] >= A);
    FB[i] = FB[i - 1] + (S[i] - S[i - 1] >= B);
  }
  X[0] = Y[0] = 1;
  for(int i = 1; i < N; ++i) {
    solve(i, A, FB, X, Y);
    solve(i, B, FA, Y, X);
  }
  cout << (X[N - 1] + Y[N - 1]) % MOD << endl;
  return 0;
}