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, L, R, p = 1000000007;
long long a[100020], A, B;
int f[100020];
int s[100020];
int main() {
	scanf("%d%lld%lld", &n, &A, &B);
	if (A > B) {
		swap(A, B);
	}
	for (int i = 1; i <= n; i++) {
		scanf("%lld", &a[i]);
	}
	for (int i = 3; i <= n; i++) {
		if (a[i] - a[i - 2] < A) {
			printf("0\n");
			return 0;
		}
	}
	a[0] = a[1] - B;
	s[1] = f[0] = 1;
	for (int i = 1; i <= n; i++) {
		while (a[i] - a[R] >= B) {
			R++;
		}
		f[i] = (s[R] - s[L] + p) % p;
		s[i + 1] = (s[i] + f[i]) % p;
		if (i > 0 && a[i] - a[i - 1] < A) {
			L = i - 1;
			R = max(R, L);
		}
	}
	printf("%d\n", (s[n + 1] - s[L] + p) % p);
	return 0;
}