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<cstring>
#include<algorithm>
#define MAXN 100000
#define INF 3000000000000000000LL
#define MO 1000000007
using namespace std;
typedef long long LL;
LL f[MAXN+5],g[MAXN+5];
LL sumf[MAXN+5],sumg[MAXN+5];
LL N,A,B,a[MAXN+5];
int main()
{
//	freopen("division.in","r",stdin);
//	freopen("division.out","w",stdout);
	scanf("%lld %lld %lld",&N,&A,&B);
	for(int i=1;i<=N;i++)
		scanf("%lld",&a[i]);
	a[N+1]=INF;
	a[0]=-INF;
	int pA=0,pB=0,pmidA=0,pmidB=0;
	sumf[2]=sumg[2]=f[0]=g[0]=1;
	for(int i=1;i<=N;i++)
	{
		if(a[i]-a[i-1]<A)
			pmidA=i;
		if(a[i]-a[i-1]<B)
			pmidB=i;
		while(a[i+1]-a[pA+1]>=A)	pA++;
		while(a[i+1]-a[pB+1]>=B)	pB++;
		if(pA==i)	pA--;
		if(pB==i)	pB--;
		int lA=pmidA-1;
		int rA=pB;
		int lB=pmidB-1;
		int rB=pA;
		if(lA<=rA)
			f[i]=(sumg[rA+2]-sumg[lA-1+2]+MO)%MO;
		if(lB<=rB)
			g[i]=(sumf[rB+2]-sumf[lB-1+2]+MO)%MO;
		sumf[i+2]=(sumf[i-1+2]+f[i])%MO;
		sumg[i+2]=(sumg[i-1+2]+g[i])%MO;
	}
	LL ans=(f[N]+g[N])%MO;
	printf("%lld\n",ans);
	return 0;
}