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;
typedef long long ll;
const int MAX=1e5+9;
ll n,dp[MAX][2],a,b,s[MAX],MOD=1e9+7,A[MAX],B[MAX];
int main()
{
	ios_base::sync_with_stdio(false),cin.tie(0),cout.tie(0);
	cin>>n>>a>>b;
	for (int i=0;i<n;i++)
	{
		cin>>s[i];
		if (!i) continue;
		if (s[i]-s[i-1]<a) A[i-1]=1;
		if (s[i]-s[i-1]<b) B[i-1]=1;
	}
	for (int i=1;i<n;i++) A[i]+=A[i-1],B[i]+=B[i-1];
	for (int i=0;i<n;i++)
	{
		int p=upper_bound(s,s+i,s[i]-a)-s;
		int flg=0;
		if (i-2>=p) flg=(i>=2?B[i-2]:0)-(p?B[p-1]:0);
		int k=0;
		for (int j=p;j<i-1;j++) if (s[j+1]-s[j]<b) k++;
		flg=!flg;
		if (!flg) dp[i][0]=0;
		else if (p==i) dp[i][0]=(dp[i-1][1]+dp[i-1][0])%MOD;
		else dp[i][0]=dp[p][1];
		int q=upper_bound(s,s+i,s[i]-b)-s;
		int flgg=0;
		if (i-2>=q) flgg=(i>=2?A[i-2]:0)-(q?A[q-1]:0);
		flgg=!flgg;
		if (!flgg) dp[i][1]=0;
		else if (q==i) dp[i][1]=(dp[i-1][0]+dp[i-1][1])%MOD;
		else dp[i][1]=dp[q][0];
		if (!i) dp[i][0]=dp[i][1]=1;	
	}
	cout<<(dp[n-1][0]+dp[n-1][1])%MOD<<endl;
	return 0;
}