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 signed int LL;
#define incID(i, l, r) for(int i = (l); i < (r); i++)
#define inc(i, n) incID(i, 0, n)

// ---- ----

const int MOD = 1000000007;
LL n, a[2], s[100000];
LL sum[2][100001], last[2], lim[2][100000];

int main() {
	cin >> n >> a[0] >> a[1];
	inc(i, n) { cin >> s[i]; }
	
	inc(k, 2) {
		int p = 0;
		inc(i, n) {
			while(s[i] - s[p] >= a[k] && p < i - 1) { p++; }
			lim[k][i] = p;
		}
	}
	
	last[0] = -1;
	last[1] = -1;
	sum[0][0] = 1;
	sum[1][0] = 1;
	
	incID(i, 1, n) {
		LL v[2];
		inc(k, 2) { v[k] = (last[1 - k] < lim[k][i] ? sum[1 - k][ lim[k][i] ] : 0); }
		inc(k, 2) {
			if(s[i] - s[i - 1] < a[k]) { last[k] = i - 1; } else { (v[k] += sum[k][i - 1]) %= MOD; }
		}
		inc(k, 2) { sum[k][i + 1] = sum[k][i] = v[k]; }
		
	}
	
	cout << (sum[0][n - 1] + sum[1][n - 1]) % MOD << endl;
	
	return 0;
}