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:
//start:13:35
#include <bits/stdc++.h>
using namespace std;
#define int long long
int n;
const int inf=5e18;
const int mod=1e9+7;
const int N=1e5+100;
int a[N],sum[N],dp[N],A,B,bef[N];
signed main(){
	cin >> n >> A >> B;
	if (A<B) swap(A,B);
	for (int i=1;i<=n;i++) cin >> a[i];
	bef[1]=bef[2]=0;
	for (int i=3;i<=n+1;i++){
		if (a[i-1]-a[i-2]>=B) bef[i]=bef[i-1];
		else bef[i]=i-2;
	}
//	for (int i=1;i<=n+1;i++) cout << bef[i] << ' ';cout << endl;
	a[0]=-inf,a[n+1]=inf;
	for (int i=1;i<=n-2;i++){
		if (a[i+2]-a[i]<B){
			cout << 0 << endl;
			return 0;
		}
	}
	dp[0]=1,sum[0]=1;
	for (int i=1;i<=n+1;i++){
		int j=upper_bound(a,a+1+n,a[i]-A)-a-1;
		if (j>=bef[i]-1) dp[i]=(sum[j]-(bef[i]?sum[bef[i]-1]:0)+mod*2)%mod;
//		if (dp[i]<0) dp[i]=0;
		sum[i]=(sum[i-1]+dp[i])%mod;
//		cout << i << ":" << dp[i] << ' ' << sum[i] << endl;
	}
//	for (int i=1;i<=n;i++) cout << dp[i] << ' ';cout << endl;
	cout << dp[n+1]%mod << endl;
	return 0; 
}