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<algorithm>
#define N (100009)
#define MOD (1000000007);
using namespace std;
long long n,a,b,r,sum,s[N],f[N];
int main()
{
	scanf("%lld%lld%lld",&n,&a,&b);
	if (a>b) swap(a,b);
	for (int i=1; i<=n; ++i)
		scanf("%lld",&s[i]);
	for (int i=3; i<=n; ++i)
		if (s[i]-s[i-2]<a){puts("0"); return 0;}
	f[0]=1; s[0]=-b; sum=0; r=0;
	for (int i=1; i<=n; ++i)
	{
		while (r<i && s[i]-s[r]>=b) sum=(sum+f[r++])%MOD;
		f[i]=sum;
		if (s[i]-s[i-1]<a) sum=0, r=i-1;
	}
	for (int i=r; i<=n; ++i)
		sum=(sum+f[i])%MOD;
	printf("%lld\n",sum);
}