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 <iostream>
#include <algorithm>
#include <cstdio>
#include <cstring>
#include <queue>
#include <vector>
#include <bitset>
#include <string>
#include <cmath>
#include <set>
#include <map>
#define Rep(i, x, y) for (int i = x; i <= y; i ++)
#define Dwn(i, x, y) for (int i = x; i >= y; i --)
#define RepE(i, x) for (int i = pos[x]; i; i = g[i].nex)
#define ev g[i].y
using namespace std;
typedef long long ll;
typedef double db;
const int N = 100010;
const int mod = 1000000007;
int n, t;
ll A, B, a[N], k, f[N];
int main()
{
	scanf ("%d%lld%lld", &n, &A, &B);
	if (A > B) swap(A, B);
	Rep(i, 1, n) scanf ("%lld", &a[i]);
	a[n + 1] = a[n] + B;
	n ++;
	t = 1, k = 1;
	Rep(i, 1, n) {
		if (i > 2 && a[i] - a[i - 2] < A) break ;
		while (a[i] - a[t] >= B) (k += f[t]) %= mod, t ++;
		f[i] = k;
		if (i > 1 && a[i] - a[i - 1] < A) t = i - 1, k = 0;
	}
	printf("%lld\n", f[n]);

	return 0;
}