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;

const int MAXN = 100005, mod = 1e9+7;
long long n, x, y;
long long a[MAXN];

int f[MAXN], g[MAXN], sumf[MAXN], sumg[MAXN];
int prex[MAXN], prey[MAXN];

int main()
{
	ios::sync_with_stdio(false);
	cin >> n >> x >> y;
	for (int i = 1; i <= n; i++) cin >> a[i];
	f[0] = g[0] = sumf[0] = sumg[0] = 1;
	a[n+1] = 1ll<<62;
	prex[1] = prey[1] = 0;
	for (int i = 2; i <= n+1; i++) {
		int px = prex[i-1], py = prey[i-1];
		while (px < i && a[i]-a[px+1] >= x) px++;
		while (py < i && a[i]-a[py+1] >= y) py++;
		prex[i] = px, prey[i] = py;
	}
	int px = 1, py = 1;
	for (int i = 1; i <= n; i++) {
		if (i > 1) {
			if (a[i]-a[i-1] < x) px = i;
			if (a[i]-a[i-1] < y) py = i;
		}
		int R = min(i-1, prey[i+1]), L = px-1;
		if (L <= R) f[i] = (L == 0 ? sumg[R] : ((sumg[R]-sumg[L-1])%mod+mod)%mod);
		R = min(i-1, prex[i+1]), L = py-1;
		if (L <= R) g[i] = (L == 0 ? sumf[R] : ((sumf[R]-sumf[L-1])%mod+mod)%mod);
		sumf[i] = (sumf[i-1]+f[i])%mod;
		sumg[i] = (sumg[i-1]+g[i])%mod;
	}
	cout << (f[n]+g[n])%mod << endl;
	return 0;
}