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>
#include<cstring>
#include<algorithm>
using namespace std;
const int p=1e9+7;
int n,f[100005],g[100005],sf[100005],sg[100005],lf[100005],lg[100005];
int prf[100005],prg[100005];
long long A,B,a[100005];
int main()
{	scanf("%d%lld%lld",&n,&A,&B);
	for(int i=1;i<=n;i++)scanf("%lld",&a[i]);
	f[1]=sf[1]=g[1]=sg[1]=lf[1]=lg[1]=1;
	prf[1]=prg[1]=0;
	for(int i=2;i<=n;i++)
	{	if(a[i]-a[i-1]<A)lf[i]=i;else lf[i]=lf[i-1];
		if(a[i]-a[i-1]<B)lg[i]=i;else lg[i]=lg[i-1];
		prf[i]=prf[i-1],prg[i]=prg[i-1];
		while(a[i]-a[prf[i]+1]>=A)++prf[i];
		while(a[i]-a[prg[i]+1]>=B)++prg[i];
		int x=min(i-1,prf[i]+1);
		if(x>=lg[i-1])f[i]=(sg[x]-sg[lg[i-1]-1]+p)%p;
			else f[i]=0;
		x=min(i-1,prg[i]+1);
		if(x>=lf[i-1])g[i]=(sf[x]-sf[lf[i-1]-1]+p)%p;
			else g[i]=0;
		sf[i]=(sf[i-1]+f[i])%p;
		sg[i]=(sg[i-1]+g[i])%p;
	}
	int ac=((sg[n]-sg[lg[n]-1]+p)%p+(sf[n]-sf[lf[n]-1]+p)%p)%p;
	printf("%d\n",ac);
	return 0;
}