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>
#include<algorithm>
#define p 1000000007
using namespace std;
int n,lasa[101010],lasb[101010];
long long a[101010],A,B,sum[101101];
int main()
{
	scanf("%d%lld%lld",&n,&A,&B);
	if(A>B) swap(A,B);
	for(int i=1;i<=n;i++)
	{
		scanf("%lld",&a[i]);
		if(i>2&&a[i]-a[i-2]<A)
		{
			puts("0");
			return 0;
		}
	}
	lasa[1]=1;
	a[0]=-0x7f7f7f7f7f7f7f7f;a[n+1]=0x7f7f7f7f7f7f7f7f;
	for(int i=2;i<=n+1;i++)
	{
		if(a[i]-a[i-1]>=A)
			lasa[i]=lasa[i-1];
		else lasa[i]=i;
		lasb[i]=upper_bound(a,a+i+1,a[i]-B)-a-1;
	}
	sum[0]=1;
	for(int i=1;i<=n+1;i++)
	{
		int l=max(0,lasa[i-1]-1),r=lasb[i];
		long long x;
		if(l>r) x=0;
		else
		{
			if(l==0)
				x=sum[r];
			else x=(sum[r]-sum[l-1]+p)%p;
		}
		sum[i]=(sum[i-1]+x)%p;
	}
	printf("%lld\n",(sum[n+1]-sum[n]+p)%p);
	return 0;
}