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;
template<typename tn> void read(tn &a){
	tn x=0,f=1; char c=' ';
	for(;!isdigit(c);c=getchar()) if(c=='-') f=-1;
	for(;isdigit(c);c=getchar()) x=x*10+c-'0';
	a=x*f;
}
const int mod = 1e9+7;
int n,s[101000],f[101000];
ll A,B,a[101000];
void upd(int &a,int b){a+=b;if(a>=mod) a-=mod;}
int main(){
	read(n);read(A);read(B);
	if(A>B) swap(A,B);
	for(int i=1;i<=n;i++){
		read(a[i]);
		if(i>2&&a[i]-a[i-2]<A){puts("0");return 0;}
		if(i>1) s[i]=s[i-1]+(a[i]-a[i-1]<A);
	}
	f[1]=1;int k=2;
	for(int i=1;i<=n;i++){
		while(k<=n&&a[k]-a[i]<B) k++;
		if(s[i]-s[i-1]==0) upd(f[i+1],f[i]);
		if(k==i+1||s[k-1]-s[i+1]==0) upd(f[k],f[i]);
	}
	cout<<f[n+1]<<'\n';
	return 0;
}