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>
typedef long long ll;
using namespace std;

ll s[100010], mod=1000000007, dp[100010][2];
int ngdist[100010][2];

int main() {
	int N;
	ll A[2];
	cin >> N >> A[0] >> A[1];
	s[0]=(-1e18)-100;
	for(int i=1; i<=N; ++i) cin >> s[i];
	for(int t=0; t<2; ++t){
		ngdist[0][t]=0;
		for(int i=1; i<=N; ++i){
			ngdist[i][t]=ngdist[i-1][t];
			if(s[i]-s[i-1]<A[t]) ++ngdist[i][t];
		}
	}
	dp[0][0]=1;
	dp[0][1]=0;
	int now[2]={0, 0};
	for(int i=1; i<=N; ++i){
		for(int t=0; t<2; ++t){
			while(s[i]-s[now[t]]>=A[t] && now[t]<i) ++now[t];
			if(now[t]==i) dp[i][t]=(dp[i-1][t]+dp[i-1][1-t])%mod;
			else if(ngdist[i-1][1-t]==ngdist[now[t]][1-t]) dp[i][t]=dp[now[t]][1-t];
			else dp[i][t]=0;
		}
	}
	cout << (dp[N][0]+dp[N][1])%mod << endl;
	return 0;
}