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 <algorithm>
#include <cstdio>
#include <cstring>
#define MOD 1000000007
using namespace std;
const int MAXN = 100005;
long long s[MAXN],a,b;
int n,limita[MAXN],d[MAXN],suf[MAXN],sum[MAXN],f[MAXN];
int main()
{
	scanf("%d%lld%lld",&n,&a,&b);
	if(a<b)swap(a,b);
	for(int i=1;i<=n;++i)
		scanf("%lld",s+i);
	int p1=0,p2=0;
	s[0]=-max(a,b);
	for(int i=1;i<=n;++i)
		if(i>2)if(s[i]-s[i-2]<b){puts("0");return 0;}
	f[0]=sum[0]=1;
	s[n+1]=(long long)2e18+100;
	for(int i=1;i<=n+1;++i){
		while(s[i]-s[p1+1]>=a && p1+1<i)++p1;
		long long o=i>=2?s[i-1]-s[i-2]:max(a,b);
		if(o<b)p2=i-1;
		if(p1>=p2-1)f[i]=(sum[p1]-(p2>=2?sum[p2-2]:0)+MOD)%MOD;
		else f[i]=0;
		sum[i]=(sum[i-1]+f[i])%MOD;
	}
	cout<<f[n+1]<<endl;
	return 0;
}