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 <iostream>
#include <vector>
#include <algorithm>
using namespace std;
typedef long long ll;
int N;
ll A,B,inf = 1e9+7;

int main(){
	cin >> N >> A >> B;
	vector<ll> S(N+1,0),dp(N+1,0);
	if(A>B) swap(A,B);
	bool judge = true;
	for(int i=1;i<=N;i++){
		cin >> S[i];
		if(i>2 && S[i]-S[i-2]<A) judge = false;
	}
	S[0] = -1;
	if(!judge){
		cout << 0 << endl;
		return 0;
	}
	dp[0] = 1;
	int id = 0;//S[i]-S[i+1]<Aとなるi
	for(int i=1;i<=N;i++){
		int s = lower_bound(S.begin(),S.end(),S[i]-B)-S.begin();
		if(S[i]-B>=0 && S[s]>S[i]-B) s--;
		if(s>=id){
			if(id>=1) (dp[i] += dp[s]-dp[id-1]+inf)%=inf;
			else (dp[i] += dp[s])%=inf;
		}
		if(S[i]-S[i-1]<A) id = i-1;
		(dp[i] += dp[i-1])%=inf;
	}
	if(id>=1) cout << (dp[N]-dp[id-1]+inf)%inf << endl;
	else cout << dp[N] << endl;
}