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<bits/stdc++.h>
#define ll long long
using namespace std;
ll getint()
{
    ll i=0,f=1;char c;
    for(c=getchar();(c!='-')&&(c<'0'||c>'9');c=getchar());
    if(c=='-')c=getchar(),f=-1;
    for(;c>='0'&&c<='9';c=getchar())i=(i<<3)+(i<<1)+c-'0';
    return i*f;
}
const int N=100005,mod=1e9+7;
int n,ans,f[N],g[N];
ll a[N],A,B;
int main()
{
	//freopen("lx.in","r",stdin);
	n=getint(),A=getint(),B=getint();
	if(A>B)swap(A,B);
	for(int i=1;i<=n;i++)a[i]=getint();
	sort(a+1,a+n+1);
	for(int i=3;i<=n;i++)if(a[i]-a[i-2]<A){puts("0");return 0;}
	f[0]=g[0]=1;int l=0,r=0;
	for(int i=1;i<=n;i++)
	{
		while(r<i-1&&a[i]-a[r+1]>=B)++r;
		if(l<=r)f[i]=(g[r]+mod-(l?g[l-1]:0))%mod;
		g[i]=(g[i-1]+f[i])%mod;
		if(i>1&&a[i]-a[i-1]<A)l=i-1;
	}
	for(int i=n;i>=0;i--)
	{
		ans=(ans+f[i])%mod;
		if(i<n&&a[i+1]-a[i]<A)break;
	}
	cout<<ans<<'\n';
	return 0;
}