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<cstdio>
using namespace std;
const int N=1e5+10,p=1e9+7;
int n,f[N],fp,fz,g[N],gp,gz;
long long A,B,s[N];
int main(){
	scanf("%d%lld%lld",&n,&A,&B);
	for (int i=1;i<=n;++i) scanf("%lld",s+i);
	s[0]=-2e18;
	f[0]=1;g[0]=1;
	for (int i=2;i<=n;++i){
		while (fp<i-2&&s[i]-s[fp+1]>=A) ++fp;
		f[i-1]=g[fp];
		while (gp<i-2&&s[i]-s[gp+1]>=B) ++gp;
		g[i-1]=f[gp];
		if (s[i]-s[i-1]<A){
			while (fz<i-1) f[fz++]=0;
		}else (f[i-1]+=f[i-2])%=p;
		if (s[i]-s[i-1]<B){
			while (gz<i-1) g[gz++]=0;
		}else (g[i-1]+=g[i-2])%=p;
	}
	printf("%d",(f[n-1]+g[n-1])%p);
	return 0;
}