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;
#define ll long long
#define f(i, x, n) for(int i = x; i < (int)n; ++i)

int md = 1e9 + 7, pr[100001], an[100001][2];
ll x[100001];

bool ok(int l, int r) { return pr[r] - pr[l - 1] == 0; }

int main(){
	int n;
	ll a, b;
	scanf("%d%lld%lld", &n, &a, &b);
	if (a > b)swap(a, b);
	f(i, 1, n + 1)scanf("%lld", x + i);
	f(i, 3, n + 1)if (x[i] - x[i - 2] < a)printf("0\n"), exit(0);
	f(i, 2, n + 1)pr[i] += pr[i - 1] + (x[i] - x[i - 1] < a);
	an[1][0] = an[1][1] = 1;
	f(i, 2, n + 1){
		int j = upper_bound(x + 1, x + i + 1, x[i] - b) - x;
		if ((an[i][1] += an[i - 1][0]) >= md)an[i][1] -= md;
		if (ok(i, i) && (an[i][1] += an[i - 1][1]) >= md)an[i][1] -= md;
		if (j == i){
			if ((an[i][0] += an[i - 1][0]) >= md)an[i][0] -= md;
			if ((an[i][0] += an[i - 1][1]) >= md)an[i][0] -= md;
		}
		else if (ok(j + 1, i - 1) && (an[i][0] += an[j][1]) >= md)an[i][0] -= md;
	}
	int o = an[n][0] + an[n][1];
	printf("%d\n", o >= md ? o - md : o);
}