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 ll;
typedef pair<int, int> PII;

#define fi first
#define se second
#define mp make_pair
#define pb push_back

#define P 1000000007
#define N 100010
int n; ll a[N], A, B;
int f[N], g[N], riA[N], riB[N];

int main() {
	cin >> n >> A >> B;
	for (int i = 0; i < n; i ++) cin >> a[i];
	riA[n-1] = riB[n-1] = n-1;
	for (int i = n-2; i >= 0; i --) {
		if (a[i+1] - a[i] >= A) riA[i] = riA[i+1];
		else riA[i] = i;
		if (a[i+1] - a[i] >= B) riB[i] = riB[i+1];
		else riB[i] = i;
	}
	f[0] = g[0] = 1;
	for (int i = 0; i < n-1; i ++) {
		// f[i]
		// first
		if (a[i+1] - a[i] >= A) {
			(f[i+1] += f[i]) %= P;
		}
		// second
		int ne = lower_bound(a, a+n, a[i]+A)-a-1;
		ne = max(ne, i+1);
		if (riB[i+1] >= ne) {
			(g[ne] += f[i]) %= P;
		}
		// g[i]
		// second
		if (a[i+1] - a[i] >= B) {
			(g[i+1] += g[i]) %= P;
		}
		// first
		ne = lower_bound(a, a+n, a[i]+B)-a-1;
		ne = max(ne, i+1);
		if (riA[i+1] >= ne) {
			(f[ne] += g[i]) %= P;
		}
	}
	printf ("%d\n", (f[n-1] + g[n-1])%P);
	return 0;
}