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>
#define ll long long
#define MN 100000
#define mod 1000000007
using namespace std;
inline ll read()
{
	ll x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
int n,g[MN+5],f[MN+5],s[MN+5];
ll a[MN+5],A,B;
int main()
{
	n=read();A=read();B=read();if(A>B) swap(A,B);
	a[0]=-5e18;s[0]=f[0]=1;
	for(int i=1;i<=n;++i) a[i]=read();a[++n]=5e18;
	for(int i=1;i+2<=n;++i) if(a[i+2]-a[i]<A) return 0*puts("0");
	for(int i=2;i<=n;++i) g[i]=a[i-1]-a[i-2]<A?i-2:g[i-1]; 
	for(int i=1,j=0;i<=n;++i)
	{
		while(j+1<i&&a[i]-a[j+1]>=B) ++j;
		int k=g[i];
		f[i]=j<k?0:(s[j]-s[k-1]+mod)%mod;
		s[i]=(s[i-1]+f[i])%mod;
	}
	printf("%d\n",f[n]);
	return 0;
}