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;
const int MAXN=100005,MOD=1000000007;
const long long LLF=0x3F3F3F3F3F3F3F3FLL;

int N;
long long A,B,S[MAXN];
int f[MAXN],sum[MAXN];

int main()
{
	scanf("%d%lld%lld",&N,&A,&B);
	for(int i=1;i<=N;i++)
		scanf("%lld",&S[i]);
	if(A>B)
		swap(A,B);
	for(int i=3;i<=N;i++)
		if(S[i]-S[i-2]<A)
		{
			puts("0");
			return 0;
		}
	S[N+1]=LLF;
	
	f[0]=sum[0]=1;
	int l=0,r=0;
	for(int i=1;i<=N+1;i++)
	{
		while(r<i-1&&S[i]-S[r+1]>=B)
			r++;
		if(l<=r)
			(f[i]+=(sum[r]-(l==0?0:sum[l-1])+MOD)%MOD)%=MOD;
		sum[i]=(sum[i-1]+f[i])%MOD;
		if(i!=1&&S[i]-S[i-1]<A)
			l=i-1;
	}
	printf("%d\n",f[N+1]);
	
	return 0;
}