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 <cstdio>
#include <iostream>
#include <algorithm>
#include <cstring>
using namespace std;
typedef long long LL;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const LL N = 1000000007;

LL n,x,y;
LL sum[200005] = {0},a[200005];
LL dp[200005],l,r;

int main(){
	cin >> n >> x >> y;
	if(x > y) swap(x,y);
	for(LL i = 1;i <= n;i ++) cin >> a[i]; a[n + 1] = INF;
	
	for(LL i = 1;i < n - 1;i ++){
		if(a[i + 2] - a[i] < x){
			cout << 0 << endl;
			return 0;
		}
	}
	
	l = 0; r = 0;
	dp[0] = 1; sum[0] = 1;
	for(LL i = 1;i <= n + 1;i ++){
		while(a[i] - a[r + 1] >= y && r <= n) r ++;
		if(l <= r) dp[i] = ((dp[i] + sum[r] - (l ? sum[l - 1] : 0)) % N + N) % N;
		sum[i] = (sum[i - 1] + dp[i]) % N;
//		cout << i << ' ' << l << ' ' << r << ' ' << dp[i] << endl;
		if(a[i] - a[i - 1] < x) l = i - 1;
	}
	
	cout << dp[n + 1] << endl;
	return 0;
}