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 <algorithm>
#define ll long long
#define rep(i,j,k) for (i=j;i<=k;i++)
#define down(i,j,k) for (i=j;i>=k;i--)
using namespace std;
const int N=1e5+5,INF=1e9,mod=1e9+7;
int n,i,j,ra[N],rb[N],la[N],lb[N];
ll A,B,s[N];
int f[N],g[N];
void updata(int &x,int y) { x+=y; if (x>=mod) x-=mod; }
int main()
{
	//freopen("division.in","r",stdin);
	//freopen("division.out","w",stdout);
	scanf("%d%lld%lld",&n,&A,&B);
	rep(i,1,n) scanf("%lld",&s[i]);
	s[n+1]=INF; ra[n]=rb[n]=ra[n+1]=rb[n+1]=n+1;
	down(i,n-1,1)
	{
		if (abs(s[i+1]-s[i])<A) ra[i]=i; else ra[i]=ra[i+1];
		if (abs(s[i+1]-s[i])<B) rb[i]=i; else rb[i]=rb[i+1];
	}
	rep(i,1,n)
	{
		la[i]=max(la[i-1],i+1);
		while (la[i]<=n && abs(s[la[i]]-s[i])<A) la[i]++;
		lb[i]=max(lb[i-1],i+1);
		while (lb[i]<=n && abs(s[lb[i]]-s[i])<B) lb[i]++;
	}
	f[1]=g[1]=1;
	rep(i,1,n-1)
	{
		if (abs(s[i+1]-s[i])>=A) updata(f[i+1],f[i]);
		if (rb[i+1]>=la[i]-1) updata(g[max(i+1,la[i]-1)],f[i]);
		if (abs(s[i+1]-s[i])>=B) updata(g[i+1],g[i]);
		if (ra[i+1]>=lb[i]-1) updata(f[max(i+1,lb[i]-1)],g[i]);
	}
	printf("%d\n",(f[n]+g[n])%mod);
	return 0;
}