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<cstdio>
#include<algorithm>
#define mod 1000000007

using namespace std;
typedef long long ll;

int n,l,r;
ll a,b,s[100001],f[100001],g[100001],ans;

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]);
	for(int i=3;i<=n;i++) 
		if(s[i]-s[i-2]<a) {putchar('0');return 0;}
	f[0]=g[0]=1;l=r=0;
	for(int i=1;i<=n;i++)
	{
		while(r<i-1 && s[i]-s[r+1]>=b) r++;
		if(l<=r) f[i]=(g[r]-(l?g[l-1]:0)+mod)%mod;
		g[i]=(g[i-1]+f[i])%mod;
		if(i>1 && s[i]-s[i-1]<a) l=i-1;
	}
	for(int i=n;i>=0;i--)
	{
		ans=(ans+f[i])%mod;
		if(i<n && s[i+1]-s[i]<a) break;
	}
	printf("%lld\n",ans);
	return 0;
}