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>
using namespace std;
const int mod=1e9+7;
long long x[1000005],dp1[1000005],dp2[1000005];
int main(){
	int n;
	long long A,B;
	scanf("%d%lld%lld",&n,&A,&B);
	for (int i=1; i<=n; i++) scanf("%lld",&x[i]);
	dp1[0]=dp2[0]=1;
	int k1=0,k2=0,k3=0,k4=0;
	for (int i=2; i<=n; i++){
		while (k1+2<i && x[i]-x[k1+1]>=A) k1++;
		while (k2+2<i && x[i]-x[k2+1]>=B) k2++;
		int sum1=dp1[k2],sum2=dp2[k1];
		dp1[i-1]=sum2;
		dp2[i-1]=sum1;
		if (x[i]-x[i-1]<A){
			while (k3<i-1) {
				dp1[k3]=0;
				k3++;
			}
		}
		else (dp1[i-1]+=dp1[i-2])%=mod;
		if (x[i]-x[i-1]<B){
			while (k4<i-1){
				dp2[k4]=0;
				k4++;
			}
		}
		else (dp2[i-1]+=dp2[i-2])%=mod;
	}
	int ans=0;
	(ans+=dp1[n-1])%=mod,(ans+=dp2[n-1])%=mod;
	printf("%d\n",ans);
	return 0;
}