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;
typedef long long ll;
const ll INF = 3e18;
const int maxn = 1e5 + 10;
const ll mod = 1e9 + 7;
int n;
ll S[maxn], f[maxn][2], g[maxn], A, B, ans;
void cmod(ll & x)
{
	while(x < 0) x += mod;
	while(x >= mod) x -= mod;
}
int main()
{
	ios::sync_with_stdio(false);
	cin >> n >> A >> B;
	if(A < B) swap(A, B);
	S[0] = -INF;
	S[n + 1] = INF;
	for(int i = 1; i <= n; ++i) cin >> S[i];
	f[0][0] = g[0] = 1;
	int L = 0, R = -1;
	for(int i = 1; i <= n; ++i) 
	{
		if(S[i] - S[i - 1] >= A) 
			f[i][0] = f[i - 1][0] + f[i - 1][1];
		cmod(f[i][0]);
		while(S[i] - S[R + 1] >= A && R + 1 < i - 1) ++R;
		//cout << i << ' ' << L << ' ' << R << endl;
		if(L <= R) f[i][1] = (R >= 0 ? g[R] : 0) - (L == 0 ? 0 : g[L - 1]);
		cmod(f[i][1]);
		g[i] = g[i - 1] + f[i][0];
		if(S[i + 1] - S[i - 1] >= B) g[i] += f[i][1];
		cmod(g[i]);
		if(S[i] - S[i - 1] < B) L = i - 1;
	}
	ans = g[n];
	for(int i = n; i; --i)
		if(S[i + 1] - S[i] < B)
		{
			ans = g[n] - g[i - 1];
			cmod(ans);
			break;
		}
	cout << ans << endl;
	return 0;
}