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>
using namespace std;

typedef long long  LL;
const int mo=int(1e9+7);
int n,f[100010],g[100010],sf[100010],sg[100010];
LL a,b,s[100010];

void work()
{
	scanf("%d %lld %lld",&n,&a,&b),s[0]=-1LL<<60;
	for (int i=1; i<=n; i++)  scanf("%lld",&s[i]);
	f[0]=g[0]=sf[0]=sg[0]=1;
	for (int i=1,fl=0,gl=0,pa=0,pb=0; i<n; i++)
		{
			while ((pa<i)&&(s[pa]<=s[i+1]-a))  pa++;
			while ((pb<i)&&(s[pb]<=s[i+1]-b))  pb++;
			f[i]=sg[pa-1],g[i]=sf[pb-1];
			if (s[i+1]-s[i]<a)  for (; fl<i; fl++)  f[fl]=sf[fl]=0;
			if (s[i+1]-s[i]<b)  for (; gl<i; gl++)  g[gl]=sg[gl]=0;
			sf[i]=(sf[i-1]+f[i])%mo,sg[i]=(sg[i-1]+g[i])%mo;
		}
	printf("%d",(sf[n-1]+sg[n-1])%mo);
}

int main()
{
	work();
	return 0;
}