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>
const int mod=1000000007;
int N;
long long A[2],S[100010];
int nxt[100010][2],lim[100010][2],f[100010][2];
int main(){
	scanf("%d%lld%lld",&N,A,A+1);
	for(int i=0;i<N;i++)scanf("%lld",S+i);
	for(int t=0;t<2;t++){
		nxt[0][t]=1;
		for(int i=1;i<N;i++){
			for(nxt[i][t]=nxt[i-1][t];nxt[i][t]<N&&S[nxt[i][t]]-S[i-1]<A[t];nxt[i][t]++);
			if(nxt[i][t]==i)nxt[i][t]++;
		}
		lim[N-1][t]=N;
		for(int i=N-1;i--;)lim[i][t]=S[i+1]-S[i]<A[t]?i+1:lim[i+1][t];
	}
	f[N][0]=f[N][1]=1;
	for(int i=N;i--;){
		for(int t=0;t<2;t++){
			f[i][t]=f[i+1][t];
			if(nxt[i][!t]<=lim[i][t])f[i][t]=(f[i][t]+f[nxt[i][!t]][!t]-f[lim[i][t]+1][!t])%mod;
			(f[i][t]+=mod)%=mod;
		}
	}
	int ans=(f[0][0]-f[1][0]+mod)%mod+(f[0][1]-f[1][1]+mod)%mod;
	printf("%d\n",ans%mod);
}