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>
using namespace std;
int n;
long long a,b;
long long e[100010];
int lsta[100010],lstb[100010];
long long dp1[100010],dp2[100010];
const long long md=1e9+7;
int lst1,lst2;
void pls(long long& x,long long y)
{
	x+=y;
	if(x>md)x-=md;
}
int main()
{
	scanf("%d%lld%lld",&n,&a,&b);
	for(int i=1;i<=n;i++)
	{
		scanf("%lld",e+i);
	}
	for(int i=2;i<=n;i++)
	{
		for(lsta[i]=lsta[i-1];e[lsta[i]+1]+a<=e[i];lsta[i]++);
		for(lstb[i]=lstb[i-1];e[lstb[i]+1]+b<=e[i];lstb[i]++);
	}
	dp1[0]=dp2[0]=1;
	for(int i=2;i<=n;i++)
	{
		long long ax=dp2[min(i-2,lsta[i])],ay=dp1[min(i-2,lstb[i])];
		if(lsta[i]!=i-1)
		{
			for(int j=lst1;j<=i-2;j++)dp1[j]=0;
			lst1=i-1;
		}
		if(lstb[i]!=i-1)
		{
			for(int j=lst2;j<=i-2;j++)dp2[j]=0;
			lst2=i-1;
		}
		pls(dp1[i-1],ax+dp1[i-2]);
		pls(dp2[i-1],ay+dp2[i-2]);
	}
	long long ans=(dp1[n-1]+dp2[n-1])%md;
	printf("%lld",ans);
	return 0;
}