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>
const int N=100005,mu=1000000007;
int n,s[N],dp[N],l=0,r=0;
long long x,y,a[N];
int main(){
	scanf("%d%lld%lld",&n,&x,&y);
	for (int i=1;i<=n;i++) scanf("%lld",&a[i]);
	if (x>y) std::swap(x,y);
	for (int i=1;i+2<=n;i++) 
		if (a[i+2]-a[i]<x){
			puts("0");return 0;
		} 
	dp[0]=s[0]=1;
	for (int i=1;i<=n;i++){
		while (a[i]-a[r+1]>=y && r<i-1) r++;
		if (l<=r){
			if (l) dp[i]=(s[r]-s[l-1]+mu)%mu;
			else dp[i]=s[r];	
		} 
		if (a[i]-a[i-1]<x) l=i-1;
		s[i]=(s[i-1]+dp[i])%mu;
	}
	int ans=0;
	for (int i=n;i>=0;i--){
		ans=(ans+dp[i])%mu;
		if (a[i+1]-a[i]<x && i<n) break;
	}
	printf("%d",ans);
}