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 Mod 1000000007
#define N 500005
using namespace std;
int n;long long a[N],A,B,dp[N],d[N];
void change(int k,int l,int r,int x,int y){
	if (l==r){d[k]+=y;d[k]%=Mod;return;}
	int mid=(l+r)>>1;if (x<=mid) change(k*2,l,mid,x,y);
	else if (x>mid) change(k*2+1,mid+1,r,x,y);
	d[k]=d[k*2]+d[k*2+1];d[k]%=Mod;
}
long long query(int k,int l,int r,int x,int y){
	if (x>y) return 0;
	if (x<=l&&y>=r) return d[k]%Mod;int mid=(l+r)>>1;
	if (y<=mid) return query(k*2,l,mid,x,y)%Mod;
	else if (x>mid) return query(k*2+1,mid+1,r,x,y)%Mod;
	else return (query(k*2,l,mid,x,mid)+query(k*2+1,mid+1,r,mid+1,y))%Mod;
}
int main(){
	scanf("%d%lld%lld",&n,&A,&B);if (A<B) swap(A,B);
	for (int i=1;i<=n;i++) scanf("%lld",&a[i]);
	sort(a+1,a+n+1);
	a[0]=-A;a[n+1]=a[n]+A;dp[0]=1;
	change(1,0,n,0,dp[0]);int l=0;int r=0;
	for (int i=1;i<=n+1;i++){
		while (a[i]-a[r+1]>=A) r++;
		if (i>=2&&a[i-1]-a[i-2]<B) l=i-2;
		if (a[i]>=a[i-1]+A) dp[i]=dp[i-1];
		dp[i]+=query(1,0,n,l,min(i-2,r));dp[i]%=Mod;
		if (i<=n&&a[i+1]-a[i-1]>=B) change(1,0,n,i,dp[i]);
	}
	printf("%lld\n",(dp[n+1]+Mod)%Mod);
	return 0;
}