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>
using namespace std;
const long long md=1e9+7;
long long n,a,b,x[100005],dp[100005][2];
vector<long long>g1,g2;
int main()
{
	cin>>n>>a>>b;
	x[1]=-(1LL<<62);
	x[n+2]=(1LL<<62);
	g1.push_back(2);
	g2.push_back(2);
	for(int i=2;i<=n+1;i++)
	{
		cin>>x[i];
		if(x[i]-x[i-1]<a)g1.push_back(i);
		if(x[i]-x[i-1]<b)g2.push_back(i);
	}
	dp[1][0]=1;
	dp[1][1]=1;
	for(int i=2;i<=n+1;i++)
	{
		int p1=upper_bound(x,x+n+3,x[i+1]-a)-x-1;
		if(p1==i)p1--;
		int p2=upper_bound(g2.begin(),g2.end(),i)-g2.begin()-1;
		p2=g2[p2]-1;
		if(p1>=p2)dp[i][0]=(dp[p1][1]-dp[p2-1][1]+md)%md;
		dp[i][0]=(dp[i][0]+dp[i-1][0])%md;
		p1=upper_bound(x,x+n+3,x[i+1]-b)-x-1;
		if(p1==i)p1--;
		p2=upper_bound(g1.begin(),g1.end(),i)-g1.begin()-1;
		p2=g1[p2]-1;
		if(p1>=p2)dp[i][1]=(dp[p1][0]-dp[p2-1][0]+md)%md;
		dp[i][1]=(dp[i][1]+dp[i-1][1])%md;
	}
	cout<<(dp[n+1][0]+dp[n+1][1]-dp[n][0]-dp[n][1]+md*2)%md<<endl;
	return 0;
}