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>
#define ll long long

using namespace std;
const int MAXN = 100005;
const int MOD = 1000000007;

ll arr[MAXN] , dp[MAXN][2] , f[MAXN][2] , g[2];

int main(){
	ios_base::sync_with_stdio(false); cin.tie(0);
	ll n,a,b; cin >> n >> g[0] >> g[1];
	for(int i=1;i<=n;i++) cin >> arr[i];
	f[1][0] = f[1][1] = 1;
	for(int i=2;i<=n;i++){
		for(int j=0;j<2;j++){
			f[i][j] = f[i-1][j];
			if(arr[i] - arr[i-1] >= g[j]) f[i][j]++;
		}
	}
	dp[1][0] = dp[1][1] = 1;
	for(int i=2;i<=n;i++){
		for(int j=0;j<2;j++){
			auto it = lower_bound(arr+1,arr+1+n,arr[i] - g[j] + 1);
			int k = it - arr;
			if(k == i) dp[i][j] = dp[i-1][0] + dp[i-1][1];
			else if(f[i-1][j^1] - f[k][j^1] == i-1-k) dp[i][j] = dp[k][j^1];
			dp[i][j] %= MOD;
			//cout << i << ' ' << j << ' ' << dp[i][j] << endl;
		}
	}
	ll ans = dp[n][0] + dp[n][1]; ans %= MOD;
	cout << ans << '\n';
	return 0;
}