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>
#define ll long long
using namespace std;
ll getint() {
	ll i = 0, f = 1;
	char c;
	for (c = getchar(); (c != '-') && (c < '0' || c > '9'); c = getchar());
	if (c == '-') c = getchar(), f = -1;
	for (; c >= '0' && c <= '9'; c = getchar())
		i = (i << 3) + (i << 1) + c - '0';
	return i * f;
}
const int N = 100005, mod = 1e9 + 7;
int n, ans, f[N], g[N];
ll a[N], A, B;
int main() {
	n = getint(), A = getint(), B = getint();
	if (A > B) swap(A, B);
	for (int i = 1; i <= n; i++) a[i] = getint();
	sort(a + 1, a + n + 1);
	for (int i = 3; i <= n; i++)
		if (a[i] - a[i - 2] < A) {
			puts("0");
			return 0;
		}
	f[0] = g[0] = 1;
	int l = 0, r = 0;
	for (int i = 1; i <= n; i++) {
		while (r < i - 1 && a[i] - a[r + 1] >= B) ++r;
		if (l <= r) f[i] = (g[r] + mod - (l ? g[l - 1] : 0)) % mod;
		g[i] = (g[i - 1] + f[i]) % mod;
		if (i > 1 && a[i] - a[i - 1] < A) l = i - 1;
	}
	for (int i = n; i >= 0; i--) {
		ans = (ans + f[i]) % mod;
		if (i < n && a[i + 1] - a[i] < A) break;
	}
	cout << ans << '\n';
	return 0;
}