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<vector>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<cmath>
#include<cstdlib>
#include<ctime>
#include<queue>
#include<set>
#include<map>
#include<stack>
using namespace std;
typedef long long LL;
const int N=2e5;
LL gi() {
	LL w=0;bool q=1;char c=getchar();
	while ((c<'0'||c>'9')&&c!='-') c=getchar();
	if (c=='-') q=0,c=getchar();
	while (c>='0'&&c<='9') w=w*10+c-'0',c=getchar();
	return q?w:-w;
}
LL s[N];
int f[N],g[N],F[N],G[N];
int main()
{
	const int mod=1e9+7;
	int n=gi()+1,i,k,ca=0,cb=0;
	LL A=gi(),B=gi();
	s[1]=-1LL<<60;for (i=2;i<=n;i++) s[i]=gi();
	f[1]=g[1]=1;
	for (i=3;i<=n;i++) {
		k=min(i-2,int(upper_bound(s+1,s+1+i,s[i]-A)-s-1));
		if (cb<k)
			(f[i-1]+=g[k]-g[cb])%=mod;

		k=min(i-2,int(upper_bound(s+1,s+1+i,s[i]-B)-s-1));
		if (ca<k)
			(g[i-1]+=f[k]-f[ca])%=mod;
		
		if (s[i]-s[i-1]<A)
			ca=i-2;
		if (s[i]-s[i-1]<B)
			cb=i-2;

		(f[i-1]+=f[i-2])%=mod;
		(g[i-1]+=g[i-2])%=mod;
	}
	printf("%d\n",int(((LL)f[n-1]-f[ca]+g[n-1]-g[cb])%mod+mod)%mod);
	
	return 0;
}