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 pb push_back
#define ll long long
using namespace std;
int main(){
	int n;
	cin>>n;
	ll a,b;
	cin>>a>>b;
	vector<ll> s(n+1), dp(n+1,0),sum(n+2);
	ll nonzero=0;
	s[0] = -1145141919123456789;
	for(int i=1;i<=n;i++){
		cin>>s[i];
	}
	dp[0]=1;
	sum[0]=0;
	sum[1]=1;
	if(a>b){
		ll x = a;
		a = b;
		b = x;
	}
	for(int i=2;i<=n;i++){
		if(s[i]-s[i-2]<a){
			cout<<0<<endl;
			return 0;
		}
	}
	
	for(int i=1;i<=n;i++){
		vector<ll>::iterator itr = upper_bound( s.begin(), s.end() , s[i] - b);
		int num = itr - s.begin();
		num--;
		if(nonzero<=num){
			dp[i] = (sum[num+1]-sum[nonzero]+mod)%mod;
		}
		//cout<<nonzero<<" "<<num<<" "<<dp[i]<<endl;
		sum[i+1] = (sum[i] + dp[i]) % mod;
		if(s[i]-s[i-1]<a){
			nonzero = i-1;
		}
	}
	cout<<(sum[n+1]-sum[nonzero]+mod)%mod<<endl;
	return 0;
}