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<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<cmath>
#include<algorithm>
#define ll long long
using namespace std;

const int N=100005;
const int mod=1000000007;
const ll inf=1000000000000000000ll;

int n,ans,l,r;
ll A,B;
int dp[N],s[N];
ll a[N];

int gs(int l,int r){
	if (l>r) return 0;
	if (l==0) return s[r];
	return (s[r]-s[l-1]+mod)%mod;
}

int main(){
	int i,j;
	scanf("%d%lld%lld",&n,&A,&B);
	if (A>B) swap(A,B);
	for (i=1;i<=n;i++) scanf("%lld",&a[i]);
	for (i=3;i<=n;i++)
		if (a[i]-a[i-2]<A){
			printf("0\n");
			return 0;
		}
	a[0]=-inf;
	dp[0]=dp[1]=1; s[1]=2; s[0]=1; l=r=0;
	for (i=2;i<=n;i++){
		while (a[i]-a[r+1]>=B) r++;
		if (a[i-1]-a[i-2]<A) l=i-2;
		dp[i]=gs(l,r);
		s[i]=(s[i-1]+dp[i])%mod;
	}
	r=n-1;
	while (a[r+1]-a[r]>=A) r--;
	printf("%d\n",gs(r,n));
	return 0;
}