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;
#define ll long long
#define MOD 1000000007
#define MAX 100100
inline ll read()
{
	ll x=0;bool t=false;char ch=getchar();
	while((ch<'0'||ch>'9')&&ch!='-')ch=getchar();
	if(ch=='-')t=true,ch=getchar();
	while(ch<='9'&&ch>='0')x=x*10+ch-48,ch=getchar();
	return t?-x:x;
}
void add(int &x,int y){x+=y;if(x>=MOD)x-=MOD;}
int n,f[MAX],s[MAX];
ll A,B,a[MAX];
int main()
{
	n=read();A=read();B=read();if(A>B)swap(A,B);
	for(int i=1;i<=n;++i)a[i]=read();
	for(int i=1;i<=n-2;++i)
		if(a[i+2]-a[i]<A){puts("0");return 0;}
	f[0]=s[0]=1;
	for(int i=1,p=0,lim=0;i<=n;++i)
	{
		while(p<i&&a[i]-a[p+1]>=B)++p;
		if(lim<=p)add(f[i],(s[p]+MOD-(lim?s[lim-1]:0))%MOD);
		add(s[i],s[i-1]+f[i]);
		if(i>1&&a[i]-a[i-1]<A)lim=i-1;
	}
	int ans=0;
	for(int i=n;~i;--i)
	{
		add(ans,f[i]);
		if(i<n&&a[i+1]-a[i]<A)break;
	}
	printf("%d\n",ans);
	return 0;
}