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 <bits/stdc++.h>
using namespace std;
#define ll long long
#define N ((ll)101*1000)
#define MOD ((ll)1e9+7)

int n;
ll A,B,a[N],dp[2][N];

int main()
{
	scanf("%lld%lld%lld",&n,&A,&B);
	for(int i=0;i<n;i++)scanf("%lld",&a[i]);
	dp[0][0]=dp[1][0]=1;
	set <pair<ll,int> > difA,difB;
	for(int i=1,jA=0,jB=0;i<n;i++)
	{
		if(i>=2 && jA<i-1)difA.insert({a[i-1]-a[i-2],i-1});
		if(i>=2 && jB<i-1)difB.insert({a[i-1]-a[i-2],i-1});
		while(jA<i && a[i]-a[jA]>=A)
		{
			difA.erase({a[jA+1]-a[jA],jA+1});jA++;
		}
		while(jB<i && a[i]-a[jB]>=B)
		{
			difB.erase({a[jB+1]-a[jB],jB+1});jB++;
		}
		if(jA==i)dp[0][i]=dp[0][i-1]+dp[1][i-1];
		else if(!difA.size() || difA.begin()->first>=B)dp[0][i]=dp[1][jA];
		if(jB==i)dp[1][i]=dp[0][i-1]+dp[1][i-1];
		else if(!difB.size() || difB.begin()->first>=A)dp[1][i]=dp[0][jB];
		if(dp[0][i]>=MOD)dp[0][i]-=MOD;
		if(dp[1][i]>=MOD)dp[1][i]-=MOD;
	}
	ll ans=(dp[0][n-1]+dp[1][n-1])%MOD;
	printf("%lld\n",ans);
	return 0;
}