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>
using namespace std;
long long n,a,b,s[200000],f[200000],g[200000],mod=1000000007;
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);
	s[0]=-b;
	f[0]=g[0]=1;
	for(int i=2;i<n;i++)
		if(s[i+1]-s[i-1]<a){puts("0");return 0;}
	long long sf=0,sg=0,pf=0,pg=0;
	for(int i=2;i<=n;i++)
	{
		for(;pf<i-1&&s[i]-s[pf]>=a;pf++)sf=(sf+f[pf])%mod;
		for(;pg<i-1&&s[i]-s[pg]>=b;pg++)sg=(sg+g[pg])%mod;
		f[i-1]=sg;g[i-1]=sf;
		if(s[i]-s[i-1]<b)sf=0,pf=i-1;
		if(s[i]-s[i-1]<a)sg=0,pg=i-1;
		//printf("sf=%lld,sg=%lld,pf=%lld,pg=%lld\n",sf,sg,pf,pg);
	}
	for(int i=pf;i<n;i++)sf=(sf+f[i])%mod;
	for(int i=pg;i<n;i++)sg=(sg+g[i])%mod;
	printf("%lld\n",(sf+sg)%mod);
	//printf("pf=%lld,pg=%lld\n",pf,pg);
	//for(int i=0;i<=n;i++)printf("(f,g)[%d]=%lld,%lld\n",i,f[i],g[i]);
	return 0;
}